{"id":935,"date":"2012-05-02T23:51:26","date_gmt":"2012-05-02T14:51:26","guid":{"rendered":"http:\/\/math.co.jp\/blog\/?p=935"},"modified":"2012-05-03T19:24:24","modified_gmt":"2012-05-03T10:24:24","slug":"%e6%95%b0%e5%ad%a6%e3%81%ae%e7%97%85%e6%b0%97","status":"publish","type":"post","link":"https:\/\/math.co.jp\/blog\/?p=935","title":{"rendered":"\u6570\u5b66\u306e\u75c5\u6c17"},"content":{"rendered":"<p>\u3088\u304f\u3042\u308b\u53d7\u9a13\u751f\u306e\u73fe\u8c61\u3092\u8a18\u9332\u3057\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3046\u3002<\/p>\n<p>\u3010\u8a18\u53f7\u8ca0\u3051\u3011<br \/>\n\u975e\u5e38\u306b\u7c21\u5358\u306a\u3053\u3068\u3092\u8a00\u3063\u3066\u3044\u308b\u306b\u3082\u95a2\u308f\u3089\u305a\u3001\u305d\u308c\u3092\u8a18\u53f7\u3067\u8868\u73fe\u3059\u308b\u3068\u308f\u304b\u3089\u306a\u304f\u306a\u3063\u305f\u308a\u3001\u8a18\u53f7\u3092\u4f7f\u3046\u3068\u308f\u3051\u306e\u308f\u304b\u3089\u306a\u3044\u3053\u3068\u3092\u3059\u308b\u73fe\u8c61\u3002<br \/>\n\u4f8b\u3048\u3070\u3001<br \/>\n1\/a + 1\/b = 1\/(a+b) \u306b\u306a\u3089\u306a\u3044\u3053\u3068\u304f\u3089\u3044\u306f\u627f\u77e5\u3057\u3066\u3044\u308b\u306e\u306b\u3001<br \/>\n\u03a3_(k=1)^n 1\/(k(k+1))=1\/(1\/3 n(n+1)(n+2))<br \/>\n\u3068\u3057\u3066\u3057\u307e\u3046\u3002<\/p>\n<p>\u6700\u8fd1\u306e\u4f8b\u3067\u306f\u3001\u6771\u5de5\u5927\u306e\u554f\u984c<\/p>\n<p>\u300c\u03a3_(n=0)^99 3^n \u306e\u6841\u6570\u3092\u6c42\u3081\u3088\u3002\u300d<\/p>\n<p>\u306b\u5bfe\u3057\u3066\u3001<br \/>\n\u300c\u03a3_(n=0)^99 (3^n \u306e\u6841\u6570)\u300d<br \/>\n\u306a\u3069\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u3063\u305f\u3002<\/p>\n<p>\u3010\u8a18\u53f7\u795e\u7d4c\u75c7\u3011<br \/>\n\u3053\u306e\u8a18\u53f7\u306f\u7528\u3044\u3066\u3088\u3044\u306e\u304b\u3001\u3068\u304b\u3001\u4f7f\u3063\u3066\u3088\u3044\u306e\u304b\u3068\u304b\u3070\u304b\u308a\u6c17\u306b\u3057\u3066\u3001\u672c\u8cea\u7684\u306a\u7b54\u6848\u3092\u66f8\u3051\u306a\u3044\u72b6\u614b\u3067\u3044\u308b\u75c5\u6c17\u3002<br \/>\n\u4f8b\u3048\u3070\u3001<br \/>\n\u300c\u7b54\u6848\u306b\u300e1\u6b21\u72ec\u7acb\u300f\u3068\u3044\u3046\u7528\u8a9e\u3092\u7528\u3044\u3066\u3088\u3044\u3067\u3059\u304b?\u300d<br \/>\n\u306e\u3088\u3046\u306a\u3053\u3068\u3070\u304b\u308a\u306b\u60a9\u3093\u3067\u3044\u308b\u72b6\u614b\u3002<\/p>\n<p>\u3010\u5916\u7a4d\u75c5\u3011<br \/>\n\u6388\u696d\u4e2d\u306b\u30d9\u30af\u30c8\u30eb\u306e\u5916\u7a4d\u306e\u8a71\u304c\u51fa\u308b\u3068\u3001\u300c\u3053\u306e\u5148\u751f\u3059\u3054\u3044\u300d\u3068\u52d8\u9055\u3044\u3057\u305f\u308a\u3001\u300c\u81ea\u5206\u306f\u9ad8\u5ea6\u306a\u5185\u5bb9\u306b\u89e6\u308c\u3066\u3044\u308b\u300d\u3068\u52d8\u9055\u3044\u3057\u3001\u8208\u596e\u3059\u308b\u75c5\u6c17\u3002\u5b9f\u969b\u306e\u3068\u3053\u308d\u3001\u7a7a\u9593\u5185\u306e\u5e73\u884c\u3067\u306a\u30442\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u3092\u51fa\u3059\u3060\u3051\u306b\u7528\u3044\u3089\u308c\u308b\u3060\u3051\u304c\u307b\u3068\u3093\u3069\u306a\u306e\u306b\u5916\u7a4d\u3092\u6df1\u304f\u5b66\u3093\u3060\u6c17\u306b\u306a\u308b\u4eba\u3082\u591a\u3044\u3002<br \/>\n\u5916\u7a4d\u75c5\u306b\u304b\u304b\u3063\u305f\u53d7\u9a13\u751f\u306f\u8208\u596e\u3057\u306a\u304c\u3089\u6b21\u306e\u3088\u3046\u306a\u8cea\u554f\u3092\u3057\u305f\u304f\u306a\u308b\u3002\u300c\u5916\u7a4d\u3063\u3066\u8a66\u9a13\u3067\u4f7f\u3063\u3066\u3044\u3044\u306e\u3067\u3059\u304b?\u300d\u3000\u79c1\u306e\u8457\u66f8\u306e\u30d9\u30af\u30c8\u30eb\u306b\u3082\u66f8\u3044\u3066\u304a\u3044\u305f\u304c\u3001\u5916\u7a4d\u3092\u8868\u3060\u3063\u3066\u4f7f\u308f\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u5834\u9762\u306f\u307b\u3068\u3093\u3069\u306a\u3044\u3002\u9670\u3067\u3046\u307e\u304f\u4f7f\u3048\u3070\u3088\u3044\u3060\u3051\u3067\u3002\u3088\u3063\u3066\u305d\u306e\u8cea\u554f\u306f\u30ca\u30f3\u30bb\u30f3\u30b9\u3067\u3042\u308b\u3002<\/p>\n<p>\u6b21\u306f\u75c5\u6c17\u306e\u5148\u751f\u306b\u3064\u3044\u3066\u3067\u3059\u3002<\/p>\n<p>\u3010\u5dfb\u304d\u6dfb\u3048\u8b1b\u5e2b\u3011<br \/>\n\u6559\u80b2\u8005\u304c\u53d7\u9a13\u6307\u5c0e\u3059\u308b\u3068\u304d\u306b\u5fc5\u8981\u306a\u6ce8\u610f\u4e8b\u9805\u3092\u53d7\u9a13\u751f\u306b\u3082\u5f37\u8981\u3059\u308b\u6559\u54e1\u30fb\u8b1b\u5e2b\u3002\u4f8b\u3048\u3070\u300c\u5782\u7dda\u306e\u8db3\u300d\u3068\u8a00\u3046\u7528\u8a9e\u306f\u6559\u79d1\u66f8\u306b\u306f\u306a\u3044\u305f\u3081\u3001\u6559\u80b2\u8005\u304c\u516c\u5f0f\u306e\u6587\u7ae0\u3092\u66f8\u304f\u3068\u304d\u3084\u5165\u8a66\u554f\u984c\u7b49\u3092\u4f5c\u6210\u3059\u308b\u3068\u304d\u306f\u4f7f\u3044\u306b\u304f\u3044\u3002(\u666e\u901a\u306f\u5782\u7dda\u3068\u5e73\u9762\u306e\u4ea4\u70b9\u306a\u3069\u306e\u8868\u73fe\u3092\u3068\u308b) \u3057\u304b\u3057\u3001\u6559\u54e1\u81ea\u4f53\u304c\u4f7f\u3048\u306a\u3044\u304b\u3089\u3068\u3044\u3063\u3066\u53d7\u9a13\u751f\u306b\u3082\u300c\u6559\u79d1\u66f8\u306b\u306f\u306a\u3044\u7528\u8a9e\u3060\u304b\u3089\u4f7f\u3063\u3066\u306f\u30c0\u30e1\u300d\u3068\u8a00\u3063\u3066\u4f7f\u7528\u3092\u7981\u6b62\u3059\u308b\u3002\u307e\u305f\u3001\u300c\u4e00\u6b21\u72ec\u7acb\u300d\u3068\u3044\u3046\u7528\u8a9e\u306f\u6559\u79d1\u66f8\u3067\u306f\u4f7f\u308f\u308c\u306a\u3044\u306e\u3067\u3001\u6559\u80b2\u8005\u304c\u4e00\u822c\u306e\u53d7\u9a13\u751f\u306b\u8aac\u660e\u3059\u308b\u30aa\u30d5\u30a3\u30b7\u30e3\u30eb\u306a\u6587\u7ae0\u306b\u306f\u4f7f\u3048\u306a\u3044\u3002\u3057\u304b\u3057\u3001\u81ea\u5206\u9054\u304c\u4f7f\u3048\u306a\u3044\u304b\u3089\u3068\u8a00\u3063\u3066\u3001\u9ad8\u6821\u751f\u306b\u306f\u3082\u300c\u4f7f\u3063\u3066\u306f\u30c0\u30e1\u300d\u3068\u7981\u6b62\u3057\u3066\u3057\u307e\u3046\u3002\u9ad8\u6821\u751f\u305f\u3061\u306f\u3001\u52d8\u9055\u3044\u3057\u305f\u6559\u54e1\u306e\u5dfb\u304d\u6dfb\u3048\u3092\u304f\u3089\u3063\u3066\u3057\u307e\u3046\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u6559\u54e1\u81ea\u8eab\u304c\u6ce8\u610f\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3053\u3068\u3068\u3001\u9ad8\u6821\u751f\u304c\u6ce8\u610f\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3053\u3068\u306e\u533a\u5225\u304c\u3067\u304d\u306a\u3044\u6559\u54e1\u306e\u3053\u3068\u3092\u8a00\u3046\u3002\u666e\u901a\u306f\u9045\u304f\u3066\u308210\u5e74\u304f\u3089\u3044\u3067\u3053\u3053\u304b\u3089\u8131\u76ae\u3059\u308b\u304c\u3001\u6b73\u3092\u3068\u308b\u307e\u3067\u8131\u76ae\u3057\u306a\u3051\u308c\u3070\u9811\u56fa\u3055\u3082\u52a0\u308f\u3063\u3066\u304b\u306a\u308a\u624b\u3054\u308f\u3044\u3002\u8a66\u9a13\u306e\u63a1\u70b9\u3067\u306f\u3064\u307e\u3089\u306a\u3044\u3053\u3068\u306b\u3053\u3060\u308f\u3063\u3066\u6e1b\u70b9\u3059\u308b\u3088\u3046\u306b\u306a\u308b\u3002\u751f\u5f92\u9054\u306f\u3001\u672c\u8cea\u3067\u306f\u306a\u3044\u3053\u3068\u306b\u795e\u7d4c\u3092\u4f7f\u3046\u3053\u3068\u306b\u306a\u308b\u304b\u3089\u5f53\u7136\u5b66\u529b\u306f\u4f38\u3073\u306a\u3044\u3002<\/p>\n<p>\u3010\u30c1\u30e9\u898b\u305b\u8b1b\u5e2b\u3011<br \/>\n(\u5b9a\u7fa9) \u9ad8\u6821\u6570\u5b66\u306e\u6388\u696d\u3067\u3001\u5927\u5b66\u6559\u990a\u7a0b\u5ea6\u306e\u8a71\u3092\u30c1\u30e9\u30c3\u3068\u3060\u3051\u3057\u3066\u8aac\u660e\u3057\u306a\u3044\u3002\u3082\u3061\u308d\u3093\u3001\u5927\u5b66\u6559\u990a\u30ec\u30d9\u30eb\u306e\u6570\u5b66\u306e\u8a71\u306b\u89e6\u308c\u308b\u3053\u3068\u304c\u60aa\u3044\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u300c\u30c1\u30e9\u898b\u305b\u8b1b\u5e2b\u300d\u306e\u5834\u5408\u306f\u3001\u81ea\u5206\u304c\u77e5\u3063\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3060\u3051\u3092\u8a00\u3063\u3066\u3001\u7d30\u304b\u3044\u8aac\u660e\u306f\u4e00\u5207\u3057\u306a\u3044\u8b1b\u5e2b\u306e\u3053\u3068\u3067\u3042\u308b\u3002<br \/>\n\u4f8b\u3048\u3070\u3001<\/p>\n<p>(\u4f8b1)\u300c\u3053\u308c\u306f\u5916\u7a4d\u3092\u77e5\u3063\u3066\u3044\u308b\u3068\u3053\u3093\u306a\u7c21\u5358\u306b\u89e3\u3051\u308b\u3093\u3060\u300d\u3068\u89e3\u3044\u3066\u898b\u305b\u308b\u3082\u306e\u306e\u3001\u5916\u7a4d\u304c\u4f55\u306a\u306e\u304b\u3092\u8aac\u660e\u3057\u306a\u3044\u3002<\/p>\n<p>(\u4f8b2) \u300c\u3053\u308c\u306f\u95a2\u6570\u306e\u5408\u6210\u7a4d\u3092\u77e5\u3063\u3066\u3044\u308b\u3068\u7d50\u679c\u304c\u3059\u3050\u306b\u898b\u3048\u3066\u3001\u307b\u3089\u3001\u3053\u3093\u306a\u306b\u7c21\u5358\u3060\u308d!\u300d\u3068\u8a00\u3063\u3066\u5408\u6210\u7a4d\u306e\u8aac\u660e\u3092\u3057\u306a\u3044\u3002<\/p>\n<p>(\u4f8b3) (\u6570\u5b66III\u306e\u90e8\u5206\u7a4d\u5206\u306e\u6388\u696d\u3067) \u300c\u3053\u308c\u306f\u03b2\u95a2\u6570\u3068\u8a00\u3046\u3093\u3060\u3088\u3002\u3053\u306e\u7d50\u679c\u304b\u3089, \u3053\u306e\u5b9a\u7a4d\u5206\u306e\u7d50\u679c\u306f\u3053\u3046\u306a\u308b\u3093\u3060\u300d\u3068\u8a00\u3063\u3066\u3001\u03b2\u95a2\u6570\u306e\u8aac\u660e\u306f\u3057\u306a\u3044\u3002\u3000(\u751f\u5f92\u3078\u306e\u88ab\u5bb3) \u96e3\u3057\u3044\u3053\u3068\u306b\u89e6\u308c\u305f\u6c17\u306b\u306a\u308b\u3002\u3053\u3053\u307e\u3067\u306f\u3088\u3044\u304c\u3001\u300c\u304b\u3063\u3053\u3044\u3044\u300d\u3068\u601d\u3063\u3066\u3001<\/p>\n<p>\u3053\u306e\u65b9\u6cd5\u306b\u56fa\u57f7\u3059\u308b\u3002\u7d50\u679c\u3001\u8eab\u306b\u306a\u3089\u305a\u306b\u307e\u3068\u3082\u306a\u65b9\u6cd5\u3092\u7fd2\u5f97\u3067\u304d\u306a\u3044\u3067\u7d42\u308f\u308b\u3002(\u4ed6\u306e\u5148\u751f\u3078\u306e\u88ab\u5bb3) 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