{"id":29,"date":"2016-07-16T11:09:20","date_gmt":"2016-07-16T03:09:20","guid":{"rendered":"http:\/\/www.91tfboys.com\/?p=29"},"modified":"2017-01-03T21:21:52","modified_gmt":"2017-01-03T13:21:52","slug":"%e7%ba%a7%e6%95%b0%e6%95%9b%e6%95%a3%e6%80%a7%e5%88%a4%e5%88%ab%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.91tfboys.com\/?p=29","title":{"rendered":"\u7ea7\u6570\u655b\u6563\u6027\u5224\u522b\u6cd5"},"content":{"rendered":"<p>\u5bf9\u4e8e\u6b63\u9879\u7ea7\u6570\uff0c\u9996\u5148\u5224\u65adlim<sub>n-&gt;\u221e<\/sub>u<sub>n<\/sub>\u662f\u5426\u4e3a0\uff0c\u82e5\u4e0d\u4e3a0\uff0c\u5219\u7ea7\u6570\u53d1\u6563\u3002<\/p>\n<p>\u5bf9\u4e8e\u7ea7\u6570\u03a3u<sub>n<\/sub>\u800c\u8a00\uff0c\u7ea7\u6570\u6536\u655b=&gt;lim<sub>n-&gt;\u221e<\/sub>u<sub>n<\/sub>=0\uff0c\u800clim<sub>n-&gt;\u221e<\/sub>u<sub>n<\/sub>=0\u5219\u4e0d\u4e00\u5b9a\u7ea7\u6570\u6536\u655b\u3002\u6545lim<sub>n-&gt;\u221e<\/sub>u<sub>n<\/sub>=0\u53ea\u662f\u7ea7\u6570\u6536\u655b\u7684\u5fc5\u8981\u6761\u4ef6\u800c\u4e0d\u662f\u5145\u5206\u6761\u4ef6\u3002<!--more--><\/p>\n<p>\u5f53lim<sub>n-&gt;\u221e<\/sub>u<sub>n<\/sub>\u4e0d\u4e3a0\u65f6\uff0c\u53ef\u4ee5\u91c7\u7528\u6bd4\u503c\u5224\u522b\u6cd5\u6216\u6839\u503c\u5224\u522b\u6cd5\u3002\u4ee4\u03c1=u<sub>n+1<\/sub>\/u<sub>n<\/sub>\u6216\u03c1=<sup>n<\/sup>\u221a(u<sub>n<\/sub>)\uff0c\u5f53\u03c1&gt;1\u6216\u03c1=+\u221e\u65f6\uff0c\u7ea7\u6570\u53d1\u6563\uff1b\u5f53\u03c1&lt;1\u65f6\uff0c\u7ea7\u6570\u6536\u655b\uff1b\u5f53\u03c1=1\u65f6\uff0c\u6b64\u5224\u522b\u6cd5\u5931\u6548\uff0c\u9700\u91c7\u7528\u5176\u5b83\u65b9\u6cd5\u3002<\/p>\n<p>\u5176\u5b83\u65b9\u6cd5\u6709\u6bd4\u8f83\u6cd5\u3001P\u7ea7\u6570\u6cd5\u7b49\u3002\u4e00\u822c\u5730\uff0c\u82e5\u6709\u4e24\u7ea7\u6570\u03a3v<sub>n<\/sub>\u548c\u03a3u<sub>n<\/sub>\u6ee1\u8db3v<sub>n<\/sub>&gt;u<sub>n<\/sub>\uff0c\u5219\u5f53\u03a3v<sub>n<\/sub>\u6536\u655b\u65f6\uff0c\u03a3u<sub>n<\/sub>\u4e5f\u6536\u655b\uff1b\u5f53\u03a3u<sub>n<\/sub>\u53d1\u6563\u65f6\uff0c\u03a3v<sub>n<\/sub>\u4e5f\u53d1\u6563\uff0c\u5373\u201c\u5927\u6536\u5c0f\u6536\uff0c\u5c0f\u53d1\u5927\u53d1\u201d\u3002\u6b64\u5916\uff0c\u2203N\uff0c\u5f53n&gt;N\u65f6\u6ee1\u8db3\uff1a\u82e5\u03a3v<sub>n<\/sub>\u6536\u655b\uff0c\u2203k\uff0cu<sub>n<\/sub>\u2264kv<sub>n<\/sub>\uff0c\u5219\u03a3u<sub>n<\/sub>\u6536\u655b\uff1b\u82e5\u03a3v<sub>n<\/sub>\u53d1\u6563\uff0c\u2203k\uff0ckv<sub>n<\/sub>\u2264u<sub>n<\/sub>\uff0c\u5219\u03a3u<sub>n<\/sub>\u53d1\u6563\u3002<\/p>\n<p>\u6bd4\u8f83\u6cd5\u4e5f\u53ef\u4ee5\u5199\u6210\u6781\u9650\u5f62\u5f0f\u3002\u4ee4<i>l<\/i>=lim<sub>n-&gt;\u221e<\/sub>(u<sub>n<\/sub>\/v<sub>n<\/sub>)\uff0c\u5219\u5f530&lt;<i>l<\/i>&lt;+\u221e\u65f6\uff0c\u4e8c\u8005\u540c\u6536\u540c\u53d1\uff1b\u5f53<i>l<\/i>=0\u65f6\uff0c\u82e5\u03a3v<sub>n<\/sub>\u6536\u655b\uff0c\u5219\u03a3u<sub>n<\/sub>\u6536\u655b\uff1b\u5f53<i>l<\/i>=+\u221e\u65f6\uff0c\u82e5\u03a3v<sub>n<\/sub>\u53d1\u6563\uff0c\u5219\u03a3u<sub>n<\/sub>\u53d1\u6563\u3002\u8fd9\u65f6\u53ef\u4ee5\u5c06\u5176\u770b\u4f5c\u662f\u65e0\u7a77\u5c0f\u6765\u5bf9\u5f85\uff0c\u901a\u8fc7\u65e0\u7a77\u5c0f\u7684\u6bd4\u9636\u6765\u5224\u65adu<sub>n<\/sub>\u548cv<sub>n<\/sub>\u7684\u5927\u5c0f\uff0c\u8fdb\u800c\u5224\u65ad\u655b\u6563\u6027\u3002<\/p>\n<p>P\u7ea7\u6570\u7684\u5f62\u5f0f\u4e3a\u03a3(1\/n<sup>p<\/sup>)\uff0c\u5f53p\u22641\u65f6\uff0c\u7ea7\u6570\u53d1\u6563\uff1b\u5f53p&gt;1\u65f6\uff0c\u7ea7\u6570\u6536\u655b\u3002\u7531\u4e0a\u53ef\u77e5\uff0c\u7ea7\u6570\u4e58\u4ee5\u4e00\u4e2a\u6570\uff0c\u4e0d\u5f71\u54cd\u5176\u655b\u6563\u6027\uff0c\u6240\u4ee5P\u7ea7\u6570\u5728\u4f7f\u7528\u65f6\u6709\u4e00\u4e9b\u53d8\u5f62\uff0c\u8fd9\u91cc\u4e0d\u518d\u4e00\u4e00\u9610\u8ff0\u3002\u5f53p=1\u65f6\u7684P\u7ea7\u6570\u53c8\u6210\u4e3a\u8c03\u548c\u7ea7\u6570\uff0c\u662f\u53d1\u6563\u7684\uff0c\u4f46\u7ea7\u6570\u03a3(-1)<sup>n-1<\/sup>(1\/n<sup>p<\/sup>)\u662f\u6536\u655b\u7684\u3002<\/p>\n<p>\u5bf9\u4e8e\u4ea4\u9519\u7ea7\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u83b1\u5e03\u5c3c\u8328\u5224\u522b\u6cd5\u3002\u5f53\u7ea7\u6570\u03a3(-1)<sup>n-1<\/sup>u<sub>n<\/sub>\u6ee1\u8db3lim<sub>n-&gt;\u221e<\/sub>(u<sub>n<\/sub>=0\u4e14u<sub>n<\/sub>&gt;u<sub>n+1<\/sub>\uff0c\u5219\u6b64\u4ea4\u9519\u7ea7\u6570\u6536\u655b\u3002\u5224\u65ad\u6761\u4ef62\u65f6\u53ef\u4ee5\u91c7\u7528\u4e8c\u8005\u76f8\u51cf\u3001\u76f8\u9664\u7b49\u65b9\u6cd5\uff0c\u4e0e0\u62161\u76f8\u6bd4\u5224\u65ad\u5927\u5c0f\uff0c\u4e5f\u53ef\u5c06\u6b64\u7ea7\u6570\u62bd\u8c61\u4e3a\u51fd\u6570<i>f<\/i>(<i>x<\/i>)\uff0c\u5f53<i>x<\/i>&gt;N\u65f6\u6ee1\u8db3<i>f<\/i>(<i>x<\/i>)\u5355\u8c03\u9012\u51cf\u5373\u53ef\u3002<\/p>\n<p>\u5bf9\u4e8e\u4e00\u822c\u9879\u7ea7\u6570\u03a3u<sub>n<\/sub>\uff0c\u6211\u4eec\u4e5f\u662f\u5148\u770b\u5f53n\u8d8b\u5411\u4e8e\u221e\u65f6u<sub>n<\/sub>\u7684\u6781\u9650\u662f\u5426\u4e3a0\uff0c\u82e5\u4e0d\u4e3a0\uff0c\u5219\u7ea7\u6570\u53d1\u6563\u3002<\/p>\n<p>\u82e5\u6781\u9650\u4e3a0\uff0c\u5219\u5224\u522b\u03a3|u<sub>n<\/sub>|\u662f\u5426\u6536\u655b\u3002\u8fd9\u65f6\u53ef\u4ee5\u4f7f\u7528\u6b63\u9879\u7ea7\u6570\u655b\u6563\u6027\u5224\u522b\u6cd5\u8fdb\u884c\u5224\u65ad\u3002\u5982\u679c\u7ea7\u6570\u6536\u655b\uff0c\u5219\u03a3u<sub>n<\/sub>\u7edd\u5bf9\u6536\u655b\uff1b\u5982\u679c\u7ea7\u6570\u53d1\u6563\uff0c\u800c\u03a3u<sub>n<\/sub>\u6761\u4ef6\u6536\u655b\u3002\u4e00\u822c\u800c\u8a00\uff0c\u5982\u679c\u7ea7\u6570\u03a3|u<sub>n<\/sub>|\u53d1\u6563\uff0c\u6211\u4eec\u4e0d\u80fd\u65ad\u5b9a\u03a3u<sub>n<\/sub>\u4e5f\u53d1\u6563\u3002\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u7528\u6bd4\u503c\u5ba1\u655b\u6cd5\u6216\u6839\u503c\u5ba1\u655b\u6cd5\u6839\u636elim<sub>n\u2192\u221e<\/sub>|u<sub>n+1<\/sub>\/u<sub>n<\/sub>|=\u03c1&gt;1\u6216lim<sub>n\u2192\u221e<\/sub><sup>n<\/sup>\u221a|u<sub>n<\/sub>|=\u03c1&gt;1\u5224\u5b9a\u03a3|u<sub>n<\/sub>|\u53d1\u6563\uff0c\u5219\u6211\u4eec\u53ef\u4ee5\u65ad\u5b9a\u03a3u<sub>n<\/sub>\u5fc5\u5b9a\u53d1\u6563\u3002\u8fd9\u662f\u56e0\u4e3a\u4ece\u03c1&gt;1\u53ef\u63a8\u77e5|u<sub>n<\/sub>|\u5728n\u2192\u221e\u65f6\u4e0d\u4e3a0\uff0c\u4ece\u800cu<sub>n<\/sub>\u5728n\u2192\u221e\u65f6\u4e0d\u4e3a0\uff0c\u56e0\u6b64\u7ea7\u6570\u03a3u<sub>n<\/sub>\u662f\u53d1\u6563\u7684\u3002<\/p>\n<p>\u5404\u9879\u90fd\u662f\u5e42\u51fd\u6570\u7684\u51fd\u6570\u9879\u7ea7\u6570\u79f0\u4e3a\u5e42\u7ea7\u6570\u3002\u03a3a<sub>n<\/sub>x<sup>n<\/sup>\u4e2da<sub>n<\/sub>\u662f\u5e42\u7ea7\u6570\u7684\u7cfb\u6570\u3002\u5f53x\u53d6\u4e0d\u540c\u7684\u503c\u65f6\u5e42\u7ea7\u6570\u5177\u6709\u4e0d\u540c\u7684\u655b\u6563\u6027\u3002\u7531\u963f\u8d1d\u5c14\uff08Abel\uff09\u5b9a\u7406\u53ef\u77e5\uff0c\u5982\u679c\u7ea7\u6570\u03a3a<sub>n<\/sub>x<sup>n<\/sup>\u5f53x=x<sub>0<\/sub>(x<sub>0<\/sub>\u22600)\u65f6\u6536\u655b\uff0c\u5219\u9002\u5408\u4e0d\u7b49\u5f0f|x|&lt;|x<sub>0<\/sub>|\u7684\u4e00\u5207x\u4f7f\u5e42\u7ea7\u6570\u7edd\u5bf9\u6536\u655b\u3002\u53cd\u4e4b\uff0c\u5982\u679c\u6280\u672f\u03a3a<sub>n<\/sub>x<sup>n<\/sup>\u5f53x=x<sub>0<\/sub>\u65f6\u53d1\u6563\uff0c\u5219\u9002\u5408\u4e0d\u7b49\u5f0f|x|&gt;|x<sub>0<\/sub>|\u7684\u4e00\u5207x\u4f7f\u5e42\u7ea7\u6570\u53d1\u6563\u3002\u7531\u6b64\u6211\u4eec\u53ef\u5f97\uff0c\u5982\u679c\u5e42\u7ea7\u6570\u03a3a<sub>n<\/sub>x<sup>n<\/sup>\u4e0d\u662f\u4ec5\u5728x=0\u4e00\u70b9\u6536\u655b\uff0c\u4e5f\u4e0d\u662f\u5728\u6574\u4e2a\u6570\u8f74\u4e0a\u90fd\u6536\u655b\uff0c\u5219\u5fc5\u6709\u4e00\u4e2a\u786e\u5b9a\u7684\u6b63\u6570R\u5b58\u5728\uff0c\u4f7f\u5f97\u5f53|x|&lt;R\u65f6\uff0c\u5e42\u7ea7\u6570\u7edd\u5bf9\u6536\u655b\uff1b\u5f53|x|&gt;R\u65f6\uff0c\u5e42\u7ea7\u6570\u53d1\u6563\uff1b\u5f53x=R\u6216x=-R\u65f6\uff0c\u5e42\u7ea7\u6570\u53ef\u80fd\u6536\u655b\u4e5f\u53ef\u80fd\u53d1\u6563\u3002\u8fd9\u4e2aR\u79f0\u4e3a\u5e42\u7ea7\u6570\u7684\u6536\u655b\u534a\u5f84\uff0c(-R, R)\u79f0\u4e3a\u7ea7\u6570\u7684\u6536\u655b\u533a\u95f4\uff0c\u518d\u7531x=\u00b1R\u65f6\u7ea7\u6570\u7684\u655b\u6563\u6027\u786e\u5b9a\u6536\u655b\u533a\u95f4\u7684\u5f00\u95ed\uff0c\u8fdb\u800c\u5f97\u5230\u6536\u655b\u57df\u3002\u5173\u4e8e\u6536\u655b\u534a\u5f84\u7684\u6c42\u6cd5\uff0c\u4ee4lim<sub>n\u2192\u221e<\/sub>|a<sub>n+1<\/sub>\/a<sub>n<\/sub>|=\u03c1\uff0c\u5219\u6536\u655b\u534a\u5f84R=1\/\u03c1\u3002\u5728\u5f97\u5230\u6536\u655b\u534a\u5f84\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u6c42\u5e42\u7ea7\u6570\u5728\u6536\u655b\u57df\u5185\u7684\u548c\u51fd\u6570\uff0c\u5728\u6b64\u4e0d\u518d\u7d2f\u8ff0\u3002<\/p>\n<p>\u6211\u4eec\u77e5\u9053\uff0c\u4efb\u4f55\u4e00\u4e2a\u51fd\u6570\u90fd\u80fd\u5199\u6210\u7531\u82e5\u5e72\u4e2a\u5e42\u51fd\u6570\u76f8\u52a0\u7684\u5f62\u5f0f\u3002\u5173\u4e8e\u51fd\u6570\u5c55\u5f00\u4e3a\u5e42\u7ea7\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5e38\u7528\u5e42\u7ea7\u6570\u5c55\u5f00\u5f0f\uff0c\u5c06\u5f85\u5c55\u5f00\u51fd\u6570\u5229\u7528\u6052\u7b49\u53d8\u5f62\uff0c\u5316\u4e3a\u5bf9\u5e94\u7684\u5f62\u5f0f\uff0c\u7136\u540e\u5957\u7528\u516c\u5f0f\u5373\u53ef\u3002<\/p>\n<p>\u603b\u7ed3\u4e00\u4e0b\uff0c\u8fd9\u4e24\u5929\u6211\u4eec\u76f8\u7ee7\u63a2\u8ba8\u4e86\u6b63\u9879\u7ea7\u6570\u3001\u4ea4\u9519\u7ea7\u6570\u3001\u4e00\u822c\u9879\u7ea7\u6570\u548c\u5e42\u7ea7\u6570\u7684\u655b\u6563\u6027\u5224\u522b\uff0c\u63a2\u8ba8\u4e86\u4e00\u4e9b\u7ea7\u6570\u655b\u6563\u6027\u5e38\u7528\u7684\u5224\u522b\u65b9\u6cd5\uff0c\u5982\u6bd4\u8f83\u5224\u522b\u6cd5\u3001\u6bd4\u503c\u5224\u522b\u6cd5\u3001\u6839\u503c\u5224\u522b\u6cd5\u7b49\uff0c\u4e86\u89e3\u4e86\u83b1\u5e03\u5c3c\u8328\u5224\u522b\u6cd5\u548c\u963f\u8d1d\u5c14\u5b9a\u7406\uff0c\u5bf9\u5e42\u7ea7\u6570\u7684\u6536\u655b\u534a\u5f84\u3001\u6536\u655b\u57df\u4e0e\u548c\u51fd\u6570\u4e5f\u8fdb\u884c\u4e86\u8ba8\u8bba\u3002\u5173\u4e8e\u5e42\u7ea7\u6570\u7684\u4e60\u9898\uff0c\u5c24\u5176\u662f\u655b\u6563\u6027\u5224\u522b\u3001\u548c\u51fd\u6570\u6c42\u89e3\u65b9\u9762\u7684\u95ee\u9898\uff0c\u53ef\u4ee5\u5341\u5206\u7075\u6d3b\uff0c\u9700\u8981\u6211\u4eec\u7ed3\u5408\u6781\u9650\u601d\u60f3\u3001\u6c42\u6781\u9650\u7684\u65b9\u6cd5\u3001\u79ef\u5206\u3001\u6c42\u5bfc\u7b49\u77e5\u8bc6\uff0c\u751a\u81f3\u4ece\u6781\u9650\u7684\u5b9a\u4e49\u51fa\u53d1\u8fdb\u884c\u63a8\u5bfc\u3002\u8fd9\u90e8\u5206\u77e5\u8bc6\u70b9\u9519\u7efc\u590d\u6742\uff0c\u8fd8\u9700\u8981\u52e4\u601d\u8003\u591a\u7ec3\u4e60\uff0c\u5c0f\u5fc3\u5165\u5751\u4e3a\u5999\u3002<\/p>\n<p>\uff08\u7531\u4e8e\u672c\u7f51\u7ad9\u95ee\u9898\uff0c\u672c\u6587\u9996\u5148\u53d1\u8868\u4e8e<a href=\"http:\/\/www.blovb.com\/\" target=\"_blank\">\u6e23\u9e1f\u5b89\u5168\u7f51\u7ad9<\/a>\uff08<a href=\"http:\/\/www.blovb.com\/\" target=\"_blank\">http:\/\/www.blovb.com\/<\/a>)\uff0c\u5206\u4e24\u6b21\u66f4\u65b0\uff0c\u5206\u522b\u4e3a<a href=\"http:\/\/www.blovb.com\/jishuliansanxingpanbiefa1\/\" target=\"_blank\">\u300a\u7ea7\u6570\u655b\u6563\u6027\u5224\u522b\u6cd5\uff08\u4e00\uff09\u300b<\/a>\u548c<a href=\"http:\/\/www.blovb.com\/jishusanlianxingpanbiefa2\/\" target=\"_blank\">\u300a\u7ea7\u6570\u655b\u6563\u6027\u5224\u522b\u6cd5\uff08\u4e8c\uff09\u300b<\/a>\uff0c\u8fd9\u6b21\u7f51\u7ad9\u66f4\u65b0\u5b8c\u6210\u540e\uff0c\u5c06\u4e24\u7bc7\u6587\u7ae0\u8fdb\u884c\u5408\u5e76\uff0c\u91cd\u53d1\u4e8e\u6b64\u3002\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5bf9\u4e8e\u6b63\u9879\u7ea7\u6570\uff0c\u9996\u5148\u5224\u65adlimn-&gt;\u221eun\u662f\u5426\u4e3a0\uff0c\u82e5\u4e0d\u4e3a0\uff0c\u5219\u7ea7\u6570\u53d1\u6563\u3002 \u5bf9\u4e8e\u7ea7\u6570\u03a3un\u800c\u8a00\uff0c\u7ea7\u6570\u6536\u655b= [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":239,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-29","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathing"],"_links":{"self":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/29","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=29"}],"version-history":[{"count":4,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/29\/revisions"}],"predecessor-version":[{"id":33,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/29\/revisions\/33"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/media\/239"}],"wp:attachment":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=29"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=29"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=29"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}