{"id":3080,"date":"2024-02-15T18:01:01","date_gmt":"2024-02-15T10:01:01","guid":{"rendered":""},"modified":"2024-02-15T18:01:01","modified_gmt":"2024-02-15T10:01:01","slug":"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0824\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5\uff08\u8865\u5145\u77e5\u8bc6\uff09","status":"publish","type":"post","link":"https:\/\/mushiming.com\/3080.html","title":{"rendered":"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0824\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5\uff08\u8865\u5145\u77e5\u8bc6\uff09"},"content":{"rendered":"<p><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"display: none;\"> \n <path stroke-linecap=\"round\" d=\"M5,0 0,2.5 5,5z\" id=\"raphael-marker-block\" style=\"-webkit-tap-highlight-color: rgba(0, 0, 0, 0);\"><\/path> \n<\/svg> <\/p>\n<div class=\"toc\">\n<h4>\u76ee\u5f55<\/h4>\n<ul>\n<li>\u524d\u8a00<\/li>\n<li>\u5f80\u671f\u6587\u7ae0<\/li>\n<li>\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5<\/li>\n<li>\n<ul>\n<li>\u4e00\u3001\u6b63\u9879\u7ea7\u6570\u53ca\u5176\u5ba1\u655b\u6cd5<\/li>\n<li>\n<ul>\n<li>\u5b9a\u4e49\uff1a\u6b63\u9879\u7ea7\u6570<\/li>\n<li>\u5b9a\u74061<\/li>\n<li>\u5b9a\u74062\uff08\u6bd4\u8f83\u5ba1\u655b\u6cd5\uff09<\/li>\n<li>\u63a8\u8bba<\/li>\n<li>\u5b9a\u74063 \uff08\u6bd4\u8f83\u5ba1\u655b\u6cd5\u7684\u6781\u9650\u5f62\u5f0f\uff09<\/li>\n<li>\u5b9a\u74064\uff08\u6bd4\u503c\u5ba1\u655b\u6cd5\uff0c\u8fbe\u6717\u8d1d\u5c14\u5224\u522b\u6cd5\uff09<\/li>\n<li>\u5b9a\u74065\uff08\u6bd4\u503c\u5ba1\u655b\u6cd5\uff0c\u67ef\u897f\u5224\u522b\u6cd5\uff09<\/li>\n<li>\u5b9a\u74066\uff08\u6781\u9650\u5ba1\u655b\u6cd5\uff09<\/li>\n<\/ul>\n<\/li>\n<li>\u4e8c\u3001\u4ea4\u9519\u7ea7\u6570\u53ca\u5176\u5ba1\u655b\u6cd5<\/li>\n<li>\n<ul>\n<li>\u5b9a\u4e49\uff1a\u4ea4\u9519\u7ea7\u6570<\/li>\n<li>\u5b9a\u74067\uff08\u83b1\u5e03\u5c3c\u8328\u5b9a\u7406\uff09<\/li>\n<\/ul>\n<\/li>\n<li>\u4e09\u3001\u7edd\u5bf9\u6536\u655b\u4e0e\u6761\u4ef6\u6536\u655b<\/li>\n<li>\n<ul>\n<li>\u5b9a\u4e49<\/li>\n<li>\u5b9a\u74068<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\u7ed3\u8bed<\/li>\n<\/ul>\n<\/div>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/aa4138e6b9b841beb29bdc47d47914c2.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0824\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5\uff08\u8865\u5145\u77e5\u8bc6\uff09 (https:\/\/mushiming.com\/)  \u7b2c1\u5f20\" title=\"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0824\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5\uff08\u8865\u5145\u77e5\u8bc6\uff09  \u7b2c1\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h2>\u524d\u8a00<\/h2>\n<blockquote>\n<p>Hello\uff01\u5c0f\u4f19\u4f34\uff01<br \/> \u975e\u5e38\u611f\u8c22\u60a8\u9605\u8bfb\u6d77\u8f70\u7684\u6587\u7ae0\uff0c\u5018\u82e5\u6587\u4e2d\u6709\u9519\u8bef\u7684\u5730\u65b9\uff0c\u6b22\u8fce\u60a8\u6307\u51fa\uff5e<br \/> &nbsp;<br \/> \u81ea\u6211\u4ecb\u7ecd <strong>\u0b18(\u0a6d\u02ca\u1d55\u02cb)\u0a6d<\/strong><br \/> \u6635\u79f0\uff1a\u6d77\u8f70<br \/> \u6807\u7b7e\uff1a\u7a0b\u5e8f\u733f\uff5cC++\u9009\u624b\uff5c\u5b66\u751f<br \/> \u7b80\u4ecb\uff1a\u56e0C\u8bed\u8a00\u7ed3\u8bc6\u7f16\u7a0b\uff0c\u968f\u540e\u8f6c\u5165\u8ba1\u7b97\u673a\u4e13\u4e1a\uff0c\u6709\u5e78\u62ff\u8fc7\u4e00\u4e9b\u56fd\u5956\u3001\u7701\u5956\u2026\u5df2\u4fdd\u7814\u3002\u76ee\u524d\u6b63\u5728\u5b66\u4e60C++\/Linux\/Python<br \/> \u5b66\u4e60\u7ecf\u9a8c\uff1a\u624e\u5b9e\u57fa\u7840 + \u591a\u505a\u7b14\u8bb0 + \u591a\u6572\u4ee3\u7801 + \u591a\u601d\u8003 + \u5b66\u597d\u82f1\u8bed\uff01<br \/> &nbsp;<br \/> \u673a\u5668\u5b66\u4e60\u5c0f\u767d\u9636\u6bb5<br \/> \u6587\u7ae0\u4ec5\u4f5c\u4e3a\u81ea\u5df1\u7684\u5b66\u4e60\u7b14\u8bb0 \u7528\u4e8e\u77e5\u8bc6\u4f53\u7cfb\u5efa\u7acb\u4ee5\u53ca\u590d\u4e60<br \/> \u77e5\u5176\u7136 \u77e5\u5176\u6240\u4ee5\u7136\uff01<\/p>\n<\/blockquote>\n<h2>\u5f80\u671f\u6587\u7ae0<\/h2>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff081\uff09\uff1a\u96c6\u5408\u4e0e\u6620\u5c04<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff082\uff09\uff1a\u7ebf\u6027\u7a7a\u95f4\u5b9a\u4e49\u53ca\u5176\u6027\u8d28<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff083\uff09\uff1a\u7ebf\u6027\u7a7a\u95f4\u7684\u57fa\u4e0e\u5750\u6807<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff084\uff09\uff1a\u57fa\u53d8\u6362\u4e0e\u5750\u6807\u53d8\u6362<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff085\uff09\uff1a\u7ebf\u6027\u5b50\u7a7a\u95f4<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff086\uff09\uff1a\u5b50\u7a7a\u95f4\u7684\u4ea4\u4e0e\u548c<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff087\uff09\uff1a\u6b27\u6c0f\u7a7a\u95f4<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff088\uff09\uff1a\u6807\u51c6\u6b63\u4ea4\u57fa\u4e0eGram-Schmidt\u8fc7\u7a0b<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff089\uff09\uff1a\u6b63\u4ea4\u8865\u4e0e\u6295\u5f71\u5b9a\u7406<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0810\uff09\uff1a\u7ebf\u6027\u53d8\u6362\u5b9a\u4e49<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0811\uff09\uff1a\u7ebf\u6027\u53d8\u6362\u7684\u77e9\u9635\u8868\u793a<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0812\uff09\uff1a\u76f8\u4f3c\u5f62\u7406\u8bba<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0813\uff09\uff1aHamliton-Cayley\u5b9a\u7406\u3001\u6700\u5c0f\u591a\u9879\u5f0f<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0814\uff09\uff1a\u5411\u91cf\u8303\u6570\u53ca\u5176\u6027\u8d28<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0815\uff09\uff1a\u77e9\u9635\u7684\u8303\u6570<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0816\uff09\uff1a\u5411\u91cf\u548c\u77e9\u9635\u7684\u6781\u9650<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0817\uff09\uff1a\u51fd\u6570\u77e9\u9635\u7684\u5fae\u5206\u548c\u79ef\u5206<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0818\uff09\uff1a\u65b9\u9635\u7684\u5e42\u7ea7\u6570<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0819\uff09\uff1a\u4e0d\u5b9a\u79ef\u5206\uff08\u8865\u5145\u77e5\u8bc6\uff09<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0820\uff09\uff1a\u65b9\u9635\u51fd\u6570<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0821\uff09\uff1a\u5e38\u7528\u65b9\u9635\u51fd\u6570\u7684\u4e00\u4e9b\u6027\u8d28<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0822\uff09\uff1a\u65b9\u9635\u51fd\u6570\u5728\u5fae\u5206\u65b9\u7a0b\u7ec4\u4e2d\u7684\u5e94\u7528<\/p>\n<p>\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0823\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u6982\u5ff5\u548c\u6027\u8d28\uff08\u8865\u5145\u77e5\u8bc6\uff09<\/p>\n<h2>\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5<\/h2>\n<h3>\u4e00\u3001\u6b63\u9879\u7ea7\u6570\u53ca\u5176\u5ba1\u655b\u6cd5<\/h3>\n<h4>\u5b9a\u4e49\uff1a\u6b63\u9879\u7ea7\u6570<\/h4>\n<p>\u4e00\u822c\u7684\u5e38\u6570\u9879\u7ea7\u6570\uff0c\u5404\u9879\u53ef\u4ee5\u4e3a\u6b63\u6570\u3001\u8d1f\u6570\u6216\u96f6<\/p>\n<p>\u5404\u9879\u90fd\u662f\u6b63\u6570\u6216\u96f6\u7684\u7ea7\u6570\uff0c\u79f0\u4e3a<strong>\u6b63\u9879\u7ea7\u6570<\/strong><\/p>\n<h4>\u5b9a\u74061<\/h4>\n<p>\u6b63\u9879\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u662f\uff1a\u5b83\u7684\u90e8\u5206\u548c\u6570\u5217<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> s n s_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.58056em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6709\u754c<\/p>\n<h4>\u5b9a\u74062\uff08\u6bd4\u8f83\u5ba1\u655b\u6cd5\uff09<\/h4>\n<p>\u8bbe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e v n \\sum_{n=1}^{\\infty}v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u90fd\u662f\u6b63\u9879\u7ea7\u6570\uff0c\u4e14<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u n \u2264 v n ( n = 1 , 2 , . . . ) u_n\\leq v_n(n=1,2,...) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.78597em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul>\n<li>\n<p>\u82e5\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e v n \\sum_{n=1}^{\\infty}v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b\uff0c\u5219\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b<\/p>\n<\/li>\n<li>\n<p>\u53cd\u4e4b\uff0c\u82e5<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53d1\u6563\uff0c\u5219<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e v n \\sum_{n=1}^{\\infty}v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53d1\u6563<\/p>\n<\/li>\n<\/ul>\n<h4>\u63a8\u8bba<\/h4>\n<p>\u5982\u679c\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e v n \\sum_{n=1}^{\\infty}v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b\uff0c\u4e14\u5b58\u5728\u6b63\u6574\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> N N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span>\uff0c\u4f7f\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n \u2265 N n\\geq N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77194em; vertical-align: -0.13597em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span>\u65f6\uff0c\u6709<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> u n \u2264 k v n ( k &gt; 0 ) u_n \\leq k v_n(k &gt; 0) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.78597em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6210\u7acb\uff0c\u90a3\u4e48\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n = 1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b<\/p>\n<p>\u5982\u679c\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e v n \\sum_{n=1}^{\\infty}v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53d1\u6563\uff0c\u4e14\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> n \u2265 N n\\geq N <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77194em; vertical-align: -0.13597em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.10903em;\">N<\/span><\/span><\/span><\/span><\/span>\u65f6\uff0c\u6709<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> u n \u2265 k v n \uff08 k &gt; 0 ) u_n \\geq k v_n\uff08k &gt; 0) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.78597em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord cjk_fallback\">\uff08<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.03148em;\">k<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6210\u7acb\uff0c\u90a3\u4e48\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n = 1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b\u53d1\u6563<\/p>\n<h4>\u5b9a\u74063 \uff08\u6bd4\u8f83\u5ba1\u655b\u6cd5\u7684\u6781\u9650\u5f62\u5f0f\uff09<\/h4>\n<p>\u8bbe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u548c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e v n \\sum_{n=1}^{\\infty}v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u90fd\u662f\u6b63\u9879\u7ea7\u6570<\/p>\n<p>\uff081\uff09 \u5982\u679c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e u n v n = l ( 0 \u2264 l &lt; + \u221e ) \\lim_{n \\rightarrow\\infty}\\frac{u_n}{v_n}=l(0\\leq l&lt; +\\infty) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.15659em; vertical-align: -0.4451em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.711492em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.164543em;\"><span class=\"\" style=\"top: -2.357em; margin-left: -0.03588em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.4101em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.164543em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.0391em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">+<\/span><span class=\"mord\">\u221e<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u4e14\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e v n \\sum_{n=1}^{\\infty}v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b\uff0c\u90a3\u4e48\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b<\/p>\n<p>\uff082\uff09\u5982\u679c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e u n v n = l ( l &gt; 0 ) \\lim_{n \\rightarrow\\infty}\\frac{u_n}{v_n}=l(l &gt; 0) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.15659em; vertical-align: -0.4451em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.711492em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.164543em;\"><span class=\"\" style=\"top: -2.357em; margin-left: -0.03588em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.4101em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.164543em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">0<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\u6216<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e u n v n = + \u221e \\lim_{n \\rightarrow\\infty}\\frac{u_n}{v_n}=+\\infty <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.15659em; vertical-align: -0.4451em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.711492em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.164543em;\"><span class=\"\" style=\"top: -2.357em; margin-left: -0.03588em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.4101em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.164543em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">+<\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span>\uff0c\u4e14\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e v n \\sum_{n=1}^{\\infty}v_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.03588em;\">v<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: -0.03588em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53d1\u6563\uff0c\u90a3\u4e48\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53d1\u6563<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/de198c608f9a4145abe72aad43980571.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0824\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5\uff08\u8865\u5145\u77e5\u8bc6\uff09 (https:\/\/mushiming.com\/)  \u7b2c2\u5f20\" title=\"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0824\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5\uff08\u8865\u5145\u77e5\u8bc6\uff09  \u7b2c2\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n<h4>\u5b9a\u74064\uff08\u6bd4\u503c\u5ba1\u655b\u6cd5\uff0c\u8fbe\u6717\u8d1d\u5c14\u5224\u522b\u6cd5\uff09<\/h4>\n<p>\u8bbe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u6b63\u9879\u7ea7\u6570\uff0c\u5982\u679c<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e u n + 1 u n = \u03c1 \\lim_{n\\rightarrow \\infty}\\frac{u_{n+1}}{u_n}=\\rho <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.94356em; vertical-align: -0.836em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -2.1em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.7em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"\"><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.10756em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.836em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u90a3\u4e48<\/p>\n<ul>\n<li>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c1 &lt; 1 \\rho&lt; 1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u65f6\uff0c\u7ea7\u6570\u6536\u655b<\/p>\n<\/li>\n<li>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c1 &gt; 1 \\rho&gt;1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u6216<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e u n + 1 u n = \u221e \\lim_{n\\rightarrow \\infty}\\frac{u_{n+1}}{u_n}=\\infty <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.19826em; vertical-align: -0.4451em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.753157em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.164543em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.143em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"><\/span><\/span><span class=\"\" style=\"top: -3.45176em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.317314em;\"><span class=\"\" style=\"top: -2.357em; margin-left: 0em; margin-right: 0.0714286em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.202521em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.4451em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"><\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span>\u65f6\u7ea7\u6570\u53d1\u6563<\/p>\n<\/li>\n<li>\n<p><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c1 = 1 \\rho = 1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u65f6\uff0c\u7ea7\u6570\u53ef\u80fd\u6536\u655b\uff0c\u4e5f\u53ef\u80fd\u53d1\u6563<\/p>\n<\/li>\n<\/ul>\n<h4>\u5b9a\u74065\uff08\u6bd4\u503c\u5ba1\u655b\u6cd5\uff0c\u67ef\u897f\u5224\u522b\u6cd5\uff09<\/h4>\n<p>\u8bbe<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u4e3a\u6b63\u9879\u7ea7\u6570\uff0c\u5982\u679c<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e u n n = \u03c1 \\lim_{n\\rightarrow\\infty}\\sqrt[n]{u_n}=\\rho <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.47416em; vertical-align: -0.7em;\"><\/span><span class=\"mop op-limits\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.69444em;\"><span class=\"\" style=\"top: -2.1em; margin-left: 0em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.7em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"\"><span class=\"mop\">lim<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.7em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord sqrt\"><span class=\"root\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.520266em;\"><span class=\"\" style=\"top: -2.80499em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size6 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.774155em;\"><span class=\"svg-align\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em;\"><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.73415em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em; height: 1.08em;\"><br \/>\n            <svg width=\"400em\" height=\"1.08em\" viewbox=\"0 0 400000 1080\" preserveaspectratio=\"xMinYMin slice\"> \n             <path d=\"M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,\n-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,\n-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,\n35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,\n-221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467\ns-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422\ns-65,47,-65,47z M834 80H400000v40H845z\"><\/path> \n            <\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.265845em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u90a3\u4e48\u5f53<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c1 &lt; 1 \\rho &lt; 1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u65f6\u7ea7\u6570\u6536\u655b<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c1 &gt; 1 \\rho &gt; 1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u6216<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e u n n = + \u221e \\lim_{n\\rightarrow\\infty}\\sqrt[n]{u_n}=+\\infty <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.04em; vertical-align: -0.31472em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord sqrt\"><span class=\"root\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.461616em;\"><span class=\"\" style=\"top: -2.74634em;\"><span class=\"pstrut\" style=\"height: 2.5em;\"><\/span><span class=\"sizing reset-size6 size1 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.72528em;\"><span class=\"svg-align\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"mord\" style=\"padding-left: 0.833em;\"><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.68528em;\"><span class=\"pstrut\" style=\"height: 3em;\"><\/span><span class=\"hide-tail\" style=\"min-width: 0.853em; height: 1.08em;\"><br \/>\n            <svg width=\"400em\" height=\"1.08em\" viewbox=\"0 0 400000 1080\" preserveaspectratio=\"xMinYMin slice\"> \n             <path d=\"M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,\n-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,\n-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,\n35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,\n-221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467\ns-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422\ns-65,47,-65,47z M834 80H400000v40H845z\"><\/path> \n            <\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.31472em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">+<\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span>\u65f6\u7ea7\u6570\u53d1\u6563<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u03c1 = 1 \\rho = 1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.625em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">\u03c1<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\u65f6\u7ea7\u6570\u53ef\u80fd\u6536\u655b\uff0c\u53ef\u80fd\u53d1\u6563<\/li>\n<\/ul>\n<h4>\u5b9a\u74066\uff08\u6781\u9650\u5ba1\u655b\u6cd5\uff09<\/h4>\n<p>\uff081\uff09\u5982\u679c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e n u n = l &gt; 0 \\lim_{n\\rightarrow\\infty} nu_n = l &gt; 0 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.0391em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u6216<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e n u n = + \u221e \\lim_{n\\rightarrow\\infty} nu_n =+\\infty <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">+<\/span><span class=\"mord\">\u221e<\/span><\/span><\/span><\/span><\/span>\uff0c\u90a3\u4e48\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53d1\u6563<\/p>\n<p>\uff082\uff09\u5982\u679c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> p &gt; 1 p &gt; 1 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.19444em;\"><\/span><span class=\"mord mathdefault\">p<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&gt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span>\uff0c\u800c<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e n p u n = l ( 0 \u2264 l &lt; + \u221e ) \\lim_{n\\rightarrow\\infty}n^p u_n = l(0 \\leq l &lt; +\\infty) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">n<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.664392em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">p<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2264<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73354em; vertical-align: -0.0391em;\"><\/span><span class=\"mord mathdefault\" style=\"margin-right: 0.01968em;\">l<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">&lt;<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">+<\/span><span class=\"mord\">\u221e<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span>\uff0c\u90a3\u4e48\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b<\/p>\n<h3>\u4e8c\u3001\u4ea4\u9519\u7ea7\u6570\u53ca\u5176\u5ba1\u655b\u6cd5<\/h3>\n<h4>\u5b9a\u4e49\uff1a\u4ea4\u9519\u7ea7\u6570<\/h4>\n<p>\u5404\u9879\u90fd\u662f\u4ea4\u9519\u7684\uff0c\u4f8b\u5982<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> u 1 \u2212 u 2 + u 3 \u2212 u 4 + . . . . . u_1 - u_2 + u_3 - u_4 + ..... <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.10556em; vertical-align: 0em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u6216<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2212 u 1 + u 2 \u2212 u 3 + u 4 \u2212 . . . . . -u_1 + u_2 - u_3 + u_4 - ..... <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">3<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.10556em; vertical-align: 0em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h4>\u5b9a\u74067\uff08\u83b1\u5e03\u5c3c\u8328\u5b9a\u7406\uff09<\/h4>\n<p>\u5982\u679c\u4ea4\u9519\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e ( \u2212 1 ) n \u2212 1 u n \\sum_{n=1}^{\\infty}(-1)^{n-1}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.11382em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">1<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.814108em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6ee1\u8db3\u6761\u4ef6<\/p>\n<p>\uff081\uff09<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> u n \u2265 u n + 1 ( n = 1 , 2 , 3 , . . . . ) u_n \\geq u_{n+1}\\quad(n = 1, 2, 3,....) <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.78597em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">\u2265<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.208331em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathdefault\">n<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em; vertical-align: -0.25em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">3<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><br \/> \uff082\uff09 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> lim \u2061 n \u2192 \u221e u n = 0 \\lim_{n\\rightarrow\\infty}u_n = 0 <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.84444em; vertical-align: -0.15em;\"><\/span><span class=\"mop\"><span class=\"mop\">lim<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">\u2192<\/span><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"><\/span><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3>\u4e09\u3001\u7edd\u5bf9\u6536\u655b\u4e0e\u6761\u4ef6\u6536\u655b<\/h3>\n<h4>\u5b9a\u4e49<\/h4>\n<p>\u4e00\u822c\u7684\u7ea7\u6570<\/p>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> u 1 + u 2 + . . . . + u n + . . . u_1 + u_2 + .... +u_n +... <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.301108em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.73333em; vertical-align: -0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.10556em; vertical-align: 0em;\"><\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u5404\u9879\u4e3a\u4efb\u610f\u5b9e\u6570<\/p>\n<p>\u5982\u679c\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5404\u9879\u7684\u7edd\u5bf9\u503c\u6240\u6784\u6210\u7684\u6b63\u9879\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e \u2223 u n \u2223 \\sum_{n=1}^{\\infty}|u_n| <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\">\u2223<\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span>\u6536\u655b<\/p>\n<p>\u90a3\u4e48\u79f0\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><font color=\"red\">\u7edd\u5bf9\u6536\u655b<\/font><\/p>\n<p>\u5982\u679c\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6536\u655b\uff0c\u800c\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u53d1\u6563<\/p>\n<p>\u5219\u79f0\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><font color=\"red\">\u6761\u4ef6\u6536\u655b<\/font><\/p>\n<h4>\u5b9a\u74068<\/h4>\n<p>\u5982\u679c\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7edd\u5bf9\u6536\u655b\uff0c\u90a3\u4e48\u7ea7\u6570<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \u2211 n = 1 \u221e u n \\sum_{n=1}^{\\infty}u_n <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.104em; vertical-align: -0.29971em;\"><\/span><span class=\"mop\"><span class=\"mop op-symbol small-op\" style=\"position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.804292em;\"><span class=\"\" style=\"top: -2.40029em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathdefault mtight\">n<\/span><span class=\"mrel mtight\">=<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.2029em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u221e<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.29971em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.166667em;\"><\/span><span class=\"mord\"><span class=\"mord mathdefault\">u<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.151392em;\"><span class=\"\" style=\"top: -2.55em; margin-left: 0em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\">n<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em;\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u5fc5\u5b9a\u6536\u655b<\/p>\n<h2>\u7ed3\u8bed<\/h2>\n<p>\u8bf4\u660e\uff1a<\/p>\n<ul>\n<li>\u53c2\u8003\u4e8e \u8bfe\u672c\u300a\u9ad8\u7b49\u6570\u5b66\u300b<\/li>\n<li>\u914d\u5408\u4e66\u4e2d\u6982\u5ff5\u8bb2\u89e3 \u7ed3\u5408\u4e86\u81ea\u5df1\u7684\u4e00\u4e9b\u7406\u89e3\u53ca\u601d\u8003<\/li>\n<\/ul>\n<p>\u6587\u7ae0\u4ec5\u4f5c\u4e3a\u5b66\u4e60\u7b14\u8bb0\uff0c\u8bb0\u5f55\u4ece0\u52301\u7684\u4e00\u4e2a\u8fc7\u7a0b<\/p>\n<p>\u5e0c\u671b\u5bf9\u60a8\u6709\u4e00\u70b9\u70b9\u5e2e\u52a9\uff0c\u5982\u6709\u9519\u8bef\u6b22\u8fce\u5c0f\u4f19\u4f34\u6307\u6b63<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/img-blog.csdnimg.cn\/0b69ad41f6394c93839bb6cd02012ee5.png\" =\"\" =\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" alt=\"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0824\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5\uff08\u8865\u5145\u77e5\u8bc6\uff09 (https:\/\/mushiming.com\/)  \u7b2c3\u5f20\" title=\"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine Learning\u7cfb\u5217\u4e4b\u77e9\u9635\u7406\u8bba\uff0824\uff09\uff1a\u5e38\u6570\u9879\u7ea7\u6570\u7684\u5ba1\u655b\u6cd5\uff08\u8865\u5145\u77e5\u8bc6\uff09  \u7b2c3\u5f20-\u7a46\u4e16\u660e\u535a\u5ba2\" ><\/p>\n","protected":false},"excerpt":{"rendered":"\u3010\u673a\u5668\u5b66\u4e60\uff5c\u6570\u5b66\u57fa\u7840\u3011Mathematics for Machine 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