{"id":12044,"date":"2023-01-02T15:41:19","date_gmt":"2023-01-02T06:41:19","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=12044"},"modified":"2023-01-09T00:34:59","modified_gmt":"2023-01-08T15:34:59","slug":"group-sequence","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/group-sequence.html","title":{"rendered":"\u7fa4\u6570\u5217\uff1a\u521d\u9805\u3084\u548c\u3001\u4e00\u822c\u9805\u306e\u8a08\u7b97\u3001\u5206\u6570\u3092\u542b\u3080\u7fa4\u6570\u5217\u306e\u89e3\u304d\u65b9"},"content":{"rendered":"\n<p>\u7279\u6b8a\u306a\u6570\u5217\u306b\u7fa4\u6570\u5217\u304c\u3042\u308a\u307e\u3059\u3002\u7fa4\u3068\u3057\u3066\u6570\u5217\u3092\u533a\u5207\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6570\u5217\u306e\u4e2d\u306b\u65b0\u305f\u306a\u6570\u5217\u304c\u751f\u307e\u308c\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u7fa4\u6570\u5217\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u7fa4\u6570\u5217\u3067\u306f\u3001\u554f\u984c\u306e\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u89e3\u304d\u65b9\u3092\u77e5\u3063\u3066\u3044\u308c\u3070\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e00\u65b9\u3067\u3001\u89e3\u304d\u65b9\u3092\u77e5\u3089\u306a\u3051\u308c\u3070\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>\u307e\u305f\u7fa4\u6570\u5217\u3092\u5b66\u3076\u3068\u304d\u3001\u6587\u7ae0\u3092\u8aad\u3093\u3067\u3082\u7406\u89e3\u3059\u308b\u306e\u306f\u96e3\u3057\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u3069\u306e\u3088\u3046\u306b\u7b54\u3048\u3092\u5f97\u308c\u3070\u3044\u3044\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u7fa4\u6570\u5217\u306e\u554f\u984c\u306e\u89e3\u304d\u65b9\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u533a\u5207\u308b\u3053\u3068\u3067\u65b0\u305f\u306a\u6570\u5217\u304c\u3067\u304d\u308b\u7fa4\u6570\u5217<\/h2>\n<p>\u6570\u5217\u3067\u306f\u3001\u898f\u5247\u6027\u3092\u3082\u3063\u3066\u6570\u5b57\u304c\u7f85\u5217\u3055\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u7fa4\u3068\u3057\u3066\u6570\u5217\u3092\u533a\u5207\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u65b0\u305f\u306a\u6570\u5217\u304c\u751f\u307e\u308c\u307e\u3059\u3002\u4f8b\u3068\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u5947\u6570\u306e\u6570\u5217\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(1,3,5,7,9,11\\)\\(,13,15\\)\\(,17,19\\)\\(,21,&#8230;\\)<\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6570\u5217\u3092\u533a\u5207\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(1|3,5|7,9,11\\)\\(|13,15\\)\\(,17,19\\)\\(|21,&#8230;\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u533a\u5207\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u65b0\u305f\u306a\u6570\u5217\u304c\u751f\u307e\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u305d\u308c\u305e\u308c\u306e\u533a\u5207\u308a\u3092\u7fa4\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u30019\u306f\u3069\u306e\u3088\u3046\u306a\u6570\u5b57\u3067\u3057\u3087\u3046\u304b\u3002\u6570\u5217\u5168\u4f53\u3067\u306f\u30019\u306f\u5de6\u304b\u30895\u756a\u76ee\u306b\u5b58\u5728\u3059\u308b\u305f\u3081\u30019\u306f\u7b2c5\u9805\u3067\u3059\u3002\u4e00\u65b9\u3067\u7fa4\u3067\u8003\u3048\u308b\u3068\u30019\u306f\u7b2c3\u7fa4\u306e\u5de6\u304b\u30892\u756a\u76ee\u306b\u5b58\u5728\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/01\/fes1.jpg\" alt=\"\" width=\"600\" height=\"111\" class=\"aligncenter size-full wp-image-12046\" 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style=\"color: #0000ff;\">\\(n-1\\)\u7fa4\u307e\u3067\u306b\u542b\u307e\u308c\u308b\u5947\u6570\u306e\u500b\u6570\u306b\u5bfe\u3057\u30661\u3092\u52a0\u3048\u308b\u3068\u3001\u300c\u7b2c\\(n\\)\u7fa4\u306e\u6700\u521d\u306e\u6570\u5b57\u304c\u5143\u306e\u6570\u5217\u3067\u4f55\u756a\u76ee\u306b\u5b58\u5728\u3059\u308b\u306e\u304b\u300d\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/01\/fes2.jpg\" alt=\"\" width=\"557\" height=\"143\" class=\"aligncenter size-full wp-image-12047\" \/><\/p>\n<p>\u7b2c\\(n\\)\u7fa4\u306f\\(n\\)\u500b\u306e\u6570\u3092\u542b\u3080\u305f\u3081\u3001\u7b2c\\(n-1\\)\u7fa4\u306f\\(n-1\\)\u500b\u306e\u6570\u3092\u542b\u307f\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u7b2c1\u7fa4\u304b\u3089\u7b2c\\(n-1\\)\u7fa4\u307e\u3067\u306b\u5b58\u5728\u3059\u308b\u5947\u6570\u306e\u500b\u6570\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(1+2+3+&#8230;+n-1\\)<\/p>\n<p>\\(=\\displaystyle\\sum_{k=1}^{n-1}{k}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{2}(n-1)n\\)<\/p>\n<p>\u7b2c1\u7fa4\u304b\u3089\u7b2c\\(n-1\\)\u7fa4\u307e\u3067\u306b\\(\\displaystyle\\frac{1}{2}(n-1)n\\)\u500b\u306e\u5947\u6570\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001<span style=\"color: #0000ff;\">\u7b2c\\(n\\)\u7fa4\u306e\u6700\u521d\u306e\u5947\u6570\u306f\u5143\u306e\u6570\u5217\u3067\\(\\displaystyle\\frac{1}{2}(n-1)n+1\\)\u756a\u76ee\u306b\u5b58\u5728\u3057\u307e\u3059\u3002<\/span><\/p>\n<p>\u5148\u307b\u3069\u8a08\u7b97\u3057\u305f\u901a\u308a\u3001\\(k\\)\u756a\u76ee\u306b\u5b58\u5728\u3059\u308b\u6570\u5b57\u3092\u5f97\u308b\u306b\u306f\u3001\u4e00\u822c\u9805\\(2k-1\\)\u3078\u4ee3\u5165\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\\(\\displaystyle\\frac{1}{2}(n-1)n+1\\)\u3092\\(2k-1\\)\u3078\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(2k-1\\)<\/p>\n<p>\\(=2\\left\\{\\displaystyle\\frac{1}{2}(n-1)n+1\\right\\}-1\\)<\/p>\n<p>\\(=(n-1)n+2-1\\)<\/p>\n<p>\\(=n^2-n+1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b2c\\(n\\)\u7fa4\u306e\u6700\u521d\u306e\u6570\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u3053\u306e\u3088\u3046\u306b\u7fa4\u6570\u5217\u306e\u8a08\u7b97\u3067\u306f\u3001\u5143\u306e\u6570\u5217\u3068\u7fa4\u306e\u4e21\u65b9\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n<p>\u6b21\u306b\u3001\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u7b2c\\(n\\)\u7fa4\u3060\u3051\u306b\u7740\u76ee\u3059\u308b\u3068\u3001\u4e00\u3064\u306e\u6570\u5217\u306b\u306a\u3063\u3066\u3044\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u5148\u307b\u3069\u8a08\u7b97\u3057\u305f\u901a\u308a\u3001\u7b2c\\(n\\)\u7fa4\u306e\u6700\u521d\u306e\u6570\u306f\\(n^2-n+1\\)\u3067\u3059\u3002\u307e\u305f\u3001\u516c\u5dee\u306f2\u3067\u3059\u3002\u7b2c\\(n\\)\u7fa4\u306b\u306f\u3001\\(n\\)\u500b\u306e\u5947\u6570\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3082\u308f\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u7b2c\\(n\\)\u7fa4\u306b\u542b\u307e\u308c\u308b\u5947\u6570\u306f\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u7b49\u5dee\u6570\u5217\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u521d\u9805\uff1a\\(n^2-n+1\\)<\/li>\n<li>\u516c\u5dee\uff1a2<\/li>\n<li>\u9805\u6570\uff1a\\(n\\)<\/li>\n<\/ul>\n<p>\u521d\u9805\\(a\\)\u3001\u516c\u5dee\\(d\\)\u3001\u9805\u6570\\(n\\)\u306e\u7b49\u5dee\u6570\u5217\u306e\u548c\\(S_n\\)\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u306b\u3088\u3063\u3066\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(S_n=\\displaystyle\\frac{1}{2}n\\{2a+(n-1)d\\}\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\u3053\u306e\u516c\u5f0f\u3078\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(S_n=\\displaystyle\\frac{1}{2}n\\{2(n^2-n+1)+(n-1)2\\}\\)<\/p>\n<p>\\(S_n=\\displaystyle\\frac{1}{2}n\u00d72n^2\\)<\/p>\n<p>\\(S_n=n^3\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u7279\u5b9a\u306e\u6570\u306e\u5834\u6240\u3092\u6c42\u3081\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u7279\u5b9a\u306e\u6570\u306b\u3064\u3044\u3066\u3001\u7b2c\u4f55\u7fa4\u306e\u4f55\u756a\u76ee\u306b\u5b58\u5728\u3059\u308b\u306e\u304b\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u5148\u307b\u3069\u306e\u5947\u6570\u306e\u6570\u5217\u306b\u3064\u3044\u3066\u3001101\u306f\u7b2c\u4f55\u7fa4\u306e\u4f55\u756a\u76ee\u306b\u5b58\u5728\u3059\u308b\u3067\u3057\u3087\u3046\u304b\u3002101\u304c\u7b2c\\(n\\)\u7fa4\u306e\\(m\\)\u756a\u76ee\u306b\u5b58\u5728\u3059\u308b\u3068\u8003\u3048\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u7b2c\\(n\\)\u7fa4\u306e\u521d\u9805\u306f\\(n^2-n+1\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001101\u306f\\(n^2-n+1\u2266101\\)\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u307e\u305f\u7b2c\\(n+1\\)\u7fa4\u306e\u521d\u9805\u306f\\((n+1)^2-(n+1)+1\\)\u3067\u3059\u3002\\((n+1)^2-(n+1)+1\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\((n+1)^2-(n+1)+1\\)<\/p>\n<p>\\(=n^2+2n+1-n\\)<\/p>\n<p>\\(=n^2+n+1\\)<\/p>\n<p>101\u306f\u7b2c\\(n+1\\)\u7fa4\u306e\u521d\u9805\u3088\u308a\u3082\u5c0f\u3055\u3044\u5024\u3067\u3042\u308b\u305f\u3081\u3001\\(101&lt;n^2+n+1\\)\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(n^2-n+1\u2266101\\)\\(&lt;n^2+n+1\\)<\/p>\n<p>\\(n^2-n\u2266100\\)\\(&lt;n^2+n\\)<\/p>\n<p>\\(n(n-1)\u2266100\\)\\(&lt;n(n+1)\\)<\/p>\n<p>\\(n=10\\)\u306e\u3068\u304d\u3001\\(9\u00d710=90\\)\u3001\\(10\u00d711=110\\)\u3068\u306a\u308a\u3001101\u306f\u7b2c10\u7fa4\u306b\u5b58\u5728\u3059\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u7b2c10\u7fa4\u306e\u521d\u9805\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(=10^2-10+1\\)<\/p>\n<p>\\(=91\\)<\/p>\n<p>\u7b2c10\u7fa4\u306f\u521d\u980591\u3001\u516c\u5dee2\u306e\u7b49\u5dee\u6570\u5217\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u7b2c10\u7fa4\u306e\\(m\\)\u756a\u76ee\u306b101\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(101=91+(m-1)\u00b72\\)<\/p>\n<p>\\(101=91+2m-2\\)<\/p>\n<p>\\(2m=12\\)<\/p>\n<p>\\(m=6\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001101\u306f\u7b2c10\u7fa4\u306e6\u756a\u76ee\u306b\u5b58\u5728\u3059\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h2>\u5206\u6570\u3092\u542b\u3080\u7fa4\u6570\u5217\u306e\u8a08\u7b97\u554f\u984c<\/h2>\n<p>\u6b21\u306b\u3001\u5206\u6570\u3092\u542b\u3080\u5834\u5408\u306e\u7fa4\u6570\u5217\u306e\u8a08\u7b97\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u5206\u6570\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u5206\u5b50\u3068\u5206\u6bcd\u306e\u898f\u5247\u6027\u3092\u5206\u3051\u3066\u8003\u3048\u308b\u3068\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u4ee5\u4e0b\u306e\u6570\u5217\u306b\u3064\u3044\u3066\u3001\u7b2c1\u9805\u304b\u3089\u7b2c210\u9805\u307e\u3067\u306e\u548c\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{1}{1},\\displaystyle\\frac{2}{2},\\displaystyle\\frac{3}{2},\\displaystyle\\frac{4}{3},\\displaystyle\\frac{5}{3},\\displaystyle\\frac{6}{3},\\)\\(\\displaystyle\\frac{7}{4},\\displaystyle\\frac{8}{4},\\)\\(\\displaystyle\\frac{9}{4},\\displaystyle\\frac{10}{4},\\)\\(\\displaystyle\\frac{11}{5},&#8230;\\)<\/li>\n<\/ul>\n<p>\u5206\u6bcd\u306b\u7740\u76ee\u3059\u308b\u3053\u3068\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u533a\u5207\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{1}{1}|\\displaystyle\\frac{2}{2},\\displaystyle\\frac{3}{2}|\\displaystyle\\frac{4}{3},\\displaystyle\\frac{5}{3},\\displaystyle\\frac{6}{3}|\\)\\(\\displaystyle\\frac{7}{4},\\displaystyle\\frac{8}{4},\\)\\(\\displaystyle\\frac{9}{4},\\displaystyle\\frac{10}{4}|\\)\\(\\displaystyle\\frac{11}{5},&#8230;\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u533a\u5207\u308b\u3068\u3001\u7b2c\\(n\\)\u7fa4\u306b\u306f\\(n\\)\u500b\u306e\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u7b2c1\u7fa4\u304b\u3089\u7b2c\\(n\\)\u7fa4\u307e\u3067\u306e\u9805\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(1+2+3+&#8230;+n\\)<\/p>\n<p>\\(=\\displaystyle\\sum_{k=1}^{n}{k}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{2}n(n+1)\\)<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u7b2c210\u9805\u306f\u7b2c\u4f55\u7fa4\u306b\u542b\u307e\u308c\u308b\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7b2c210\u9805\u304c\u7b2c\\(n\\)\u7fa4\u306b\u542b\u307e\u308c\u308b\u3068\u8003\u3048\u308b\u3068\u3001210\u306f\u7b2c\\(n-1\\)\u7fa4\u307e\u3067\u306e\u9805\u6570\u3088\u308a\u5927\u304d\u304f\u3001\u7b2c\\(n\\)\u7fa4\u307e\u3067\u306e\u9805\u6570\u4ee5\u4e0b\u3068\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1}{2}(n-1)n&lt;210\\)\\(\u2266\\displaystyle\\frac{1}{2}n(n+1)\\)<\/p>\n<p>\\((n-1)n&lt;420\\)\\(\u2266n(n+1)\\)<\/p>\n<p>\\(n=20\\)\u306e\u3068\u304d\u3001\\(19\u00d720=380\\)\u3067\u3059\u3002\u307e\u305f\u3001\\(20\u00d721=420\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u7b2c210\u9805\u306f\u7b2c20\u7fa4\u306b\u5b58\u5728\u3059\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h3>\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3057\u3001\u7b54\u3048\u3092\u5f97\u308b<\/h3>\n<p>\u6b21\u306b\u3001\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u5148\u307b\u3069\u8a08\u7b97\u3057\u305f\u901a\u308a\u3001\\(20\u00d721=420\\)\u3067\u3042\u308b\u305f\u3081\u3001\u7b2c210\u9805\u306f\u7b2c20\u7fa4\u306e\u6700\u5f8c\u306e\u6570\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u307e\u305a\u306f\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u5f97\u308b\u305f\u3081\u3001\u7b2c\\(n\\)\u7fa4\u306e\u521d\u9805\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u5143\u306e\u6570\u5217\u306b\u7740\u76ee\u3059\u308b\u3068\u3001\u7b2c\\(k\\)\u9805\u306e\u5834\u5408\u3001\u5206\u5b50\u306f\u521d\u98051\u3001\u516c\u5dee1\u306e\u516c\u5dee\u6570\u5217\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u7b2c\\(k\\)\u9805\u306e\u5206\u5b50\u306f\\(k\\)\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u3001\u7b2c1\u7fa4\u304b\u3089\u7b2c\\(n-1\\)\u7fa4\u307e\u3067\u306e\u9805\u6570\u306f\\(\\displaystyle\\frac{1}{2}(n-1)n\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u7b2c\\(n\\)\u7fa4\u306e\u521d\u9805\u306e\u9805\u6570\u306f\\(\\displaystyle\\frac{1}{2}(n-1)n+1\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u521d\u9805\u306e\u5206\u5b50\u306e\u5024\u306f\\(\\displaystyle\\frac{1}{2}(n-1)n+1\\)\u3067\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u5206\u5b50\u3060\u3051\u306b\u7740\u76ee\u3059\u308b\u3068\u3001\u7b2c\\(n\\)\u7fa4\u3067\u306f\u3001\u521d\u9805\\(\\displaystyle\\frac{1}{2}(n-1)n+1\\)\u3001\u516c\u5dee1\u3001\u9805\u6570\\(n\\)\u306e\u7b49\u5dee\u6570\u5217\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7b2c\\(n\\)\u7fa4\u3067\u306e\u5206\u5b50\u306e\u548c\\(S\\)\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<p>\\(S=\\displaystyle\\frac{1}{2}n\\{2a+(n-1)d\\}\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{1}{2}n\\{(n-1)n+2+(n-1)\u00b71\\}\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{1}{2}n(n^2-n+2+n-1)\\)<\/p>\n<p>\\(S=\\displaystyle\\frac{1}{2}n(n^2+1)\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u7b2c\\(n\\)\u7fa4\u3067\u306f\u3001\u5206\u5b50\u306e\u7dcf\u548c\u306f\\(\\displaystyle\\frac{1}{2}n(n^2+1)\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u306a\u304a\u7b2c\\(n\\)\u7fa4\u306e\u5206\u6bcd\u306f\\(n\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(n\\)\u3067\u5272\u308b\u3068\u3001\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(\\displaystyle\\frac{n^2+1}{2}\\)\u304c\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3067\u306f\u306a\u304f\u3001\u7b2c1\u7fa4\u304b\u3089\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u5f0f\u306b\u3088\u3063\u3066\u7b2c1\u7fa4\u304b\u3089\u7b2c\\(n\\)\u7fa4\u306e\u7dcf\u548c\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\sum_{k=1}^{n}{\\displaystyle\\frac{k^2+1}{2}}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{2}\\displaystyle\\sum_{k=1}^{n}{(k^2+1)}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{2}\u00b7\\displaystyle\\frac{1}{6}n(n+1)(2n+1)\\)\\(+\\displaystyle\\frac{1}{2}n\\)<\/p>\n<p>\u5148\u307b\u3069\u8a08\u7b97\u3057\u305f\u901a\u308a\u3001\\(n=20\\)\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1}{2}\u00b7\\displaystyle\\frac{20\u00d721\u00d741}{6}\\)\\(+\\displaystyle\\frac{1}{2}\u00d720\\)<\/p>\n<p>\\(=1435+10\\)<\/p>\n<p>\\(=1445\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b2c1\u7fa4\u304b\u3089\u7b2c20\u7fa4\u307e\u3067\u306e\u7dcf\u548c\uff08\u7b2c1\u9805\u304b\u3089\u7b2c210\u9805\u307e\u3067\u306e\u548c\uff09\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u5206\u6570\u3092\u542b\u3080\u7fa4\u6570\u5217\u3067\u3042\u3063\u3066\u3082\u3001\u554f\u984c\u306e\u89e3\u304d\u65b9\u306f\u540c\u3058\u3067\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<h2>\u7fa4\u6570\u5217\u306e\u89e3\u304d\u65b9\u3092\u5b66\u3076<\/h2>\n<p>\u591a\u304f\u306e\u4eba\u304c\u7fa4\u6570\u5217\u3092\u82e6\u624b\u3068\u3057\u307e\u3059\u3002\u6570\u5217\u306e\u4e2d\u306b\u6570\u5217\u304c\u73fe\u308c\u308b\u305f\u3081\u3001\u591a\u304f\u306e\u4eba\u304c\u6df7\u4e71\u3059\u308b\u306e\u3067\u3059\u3002\u305f\u3060\u7fa4\u6570\u5217\u306f\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u7fa4\u6570\u5217\u306e\u8a08\u7b97\u3067\u306f\u3001\\(n-1\\)\u7fa4\u306b\u7740\u76ee\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7b2c\\(n\\)\u7fa4\u306e\u521d\u9805\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u307e\u305f\u7b2c\\(n\\)\u7fa4\u306e\u521d\u9805\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7b2c\\(n\\)\u7fa4\u306b\u542b\u307e\u308c\u308b\u7dcf\u548c\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u7279\u5b9a\u306e\u6570\u306e\u5834\u6240\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u8a08\u7b97\u904e\u7a0b\u306f\u5206\u6570\u3092\u542b\u3080\u7fa4\u6570\u5217\u3067\u3042\u3063\u3066\u3082\u540c\u69d8\u3067\u3059\u3002\u7b2c\\(n\\)\u7fa4\u306e\u521d\u9805\u3084\u7b2c\\(n\\)\u7fa4\u306b\u542b\u307e\u308c\u308b\u7dcf\u548c\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u8907\u96d1\u306a\u8a08\u7b97\u3067\u306f\u3042\u308b\u3082\u306e\u306e\u3001\u7fa4\u6570\u5217\u306f\u554f\u984c\u306e\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u89e3\u304d\u65b9\u3092\u899a\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u3066\u7fa4\u6570\u5217\u3067\u306e\u7b54\u3048\u3092\u5f97\u308c\u3070\u3044\u3044\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7279\u6b8a\u306a\u6570\u5217\u306b\u7fa4\u6570\u5217\u304c\u3042\u308a\u307e\u3059\u3002\u7fa4\u3068\u3057\u3066\u6570\u5217\u3092\u533a\u5207\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6570\u5217\u306e\u4e2d\u306b\u65b0\u305f\u306a\u6570\u5217\u304c\u751f\u307e\u308c\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u7fa4\u6570\u5217\u3068\u3044\u3044\u307e\u3059\u3002 \u7fa4\u6570\u5217\u3067\u306f\u3001\u554f\u984c\u306e\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u89e3\u304d\u65b9\u3092\u77e5\u3063\u3066\u3044\u308c\u3070\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 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