\u6570\u5217\u306e\u8a08\u7b97\u3092\u3059\u308b\u969b\u3001\\(n\\)\u306e\u5024\u3092\u7121\u9650\u5927\u306b\u5927\u304d\u304f\u3059\u308b\u3068\u304d\u306b\u3069\u306e\u3088\u3046\u306a\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u3053\u3046\u3057\u305f\u6570\u5217\u3092\u7121\u9650\u6570\u5217\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n
\u7121\u9650\u6570\u5217\u3067\u3069\u306e\u3088\u3046\u306a\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u306e\u304b\u76f4\u611f\u3067\u5224\u65ad\u3059\u308b\u306e\u306f\u96e3\u3057\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u6570\u5217\u306e\u6975\u9650\u3067\u5f97\u3089\u308c\u308b\u7b54\u3048\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u6975\u9650\u3067\u306f\u591a\u304f\u5834\u5408\u3001\u53ce\u675f\u307e\u305f\u306f\u767a\u6563\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u305f\u3081\u3001\u3053\u308c\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u306a\u304a\u3001\u76f4\u63a5\u7684\u306a\u8a08\u7b97\u304c\u96e3\u3057\u3044\u30b1\u30fc\u30b9\u3082\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u30012\u3064\u306e\u6570\u5217\u3092\u7528\u3044\u3066\u631f\u307f\u6483\u3061\u3092\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u308b\u65b9\u6cd5\u3092\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3068\u3044\u3044\u307e\u3059\u3002\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u306b\u3088\u3063\u3066\u3082\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u3066\u6570\u5217\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7121\u9650\u6570\u5217\u306e\u57fa\u672c\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n
\u672b\u9805\u304c\u5b58\u5728\u3057\u306a\u3044\u6570\u5217\u3092\u7121\u9650\u6570\u5217\u3068\u3044\u3044\u307e\u3059\u3002\u6570\u5217\u3067\\(\\{a_n\\}\\)\u3068\u8a18\u3059\u5834\u5408\u3001\u901a\u5e38\u306f\u7121\u9650\u6570\u5217\u3092\u6307\u3057\u307e\u3059\u3002\u7121\u9650\u6570\u5217\u3067\u306f\u3001\u591a\u304f\u306e\u30b1\u30fc\u30b9\u3067\u53ce\u675f\u307e\u305f\u306f\u767a\u6563\u3057\u307e\u3059\u3002<\/p>\n
\u30fb\u7121\u9650\u6570\u5217\u3067\u306e\u53ce\u675f<\/strong><\/p>\n \u4f8b\u3048\u3070\\(\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{1}{n}\\)\u306f\u3069\u306e\u3088\u3046\u306a\u5024\u3067\u3057\u3087\u3046\u304b\u3002\\(n\\)\u306e\u5024\u3092\u7121\u9650\u5927\uff08\\(\u221e\\)\uff09\u307e\u3067\u5927\u304d\u304f\u3059\u308b\u5834\u5408\u3001\u5024\u306f\u307b\u307c0\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{1}{n}=0\\)\u3068\u8003\u3048\u307e\u3059\u3002<\/span>\u5b9f\u969b\u306b\u306f0\u3067\u306f\u306a\u3044\u3082\u306e\u306e\u30010\u3068\u307f\u306a\u3059\u306e\u3067\u3059\u3002<\/p>\n \u307e\u305f\\(\\displaystyle \\lim_{ n \\to \\infty } \\left(\\displaystyle\\frac{1}{n}+2\\right)\\)\u306b\u3064\u3044\u3066\u306f\u3001\\(\\displaystyle\\frac{1}{n}\\)\u304c0\u306b\u306a\u308b\u305f\u3081\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } \\left(\\displaystyle\\frac{1}{n}+2\\right)=2\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u7279\u5b9a\u306e\u5024\u306b\u53ce\u675f\u3057\u3066\u3044\u304f\u306e\u3067\u3059\u3002<\/p>\n \u30fb\u7121\u9650\u6570\u5217\u3067\u306e\u767a\u6563<\/strong><\/p>\n \u4e00\u65b9\u3001\u7121\u9650\u306b\u5024\u304c\u5927\u304d\u304f\u306a\u308b\uff08\u307e\u305f\u306f\u5c0f\u3055\u304f\u306a\u308b\uff09\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } n=\u221e\\)\u3068\u306a\u308a\u307e\u3059\u3002\\(n\\)\u306e\u5024\u304c\u7121\u9650\u5927\u306b\u5927\u304d\u304f\u306a\u308b\u5834\u5408\u3001\u7b54\u3048\u306f\\(\u221e\\)\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u65b9\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } -n=-\u221e\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n \u6570\u5217\\(\\{a_n\\}\\)\u304c\u7279\u5b9a\u306e\u5024\u306b\u53ce\u675f\u3057\u306a\u3044\u5834\u5408\u3001\u6b63\u307e\u305f\u306f\u8ca0\u306b\u767a\u6563\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u7b2c\\(n\\)\u9805\u304c\\(5n-n^2\\)\u306e\u5834\u5408\u3001\u6570\u5217\u306e\u6975\u9650\u306f\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(\\displaystyle \\lim_{ n \\to \\infty } (5n-n^2)\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } n^2\\left(\\displaystyle\\frac{1}{n}-1\\right)\\)<\/p>\n \\(=\u221e(0-1)\\)<\/p>\n \\(=-\u221e\\)<\/p>\n \u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u306f\\(-\u221e\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n \u53c2\u8003\u307e\u3067\u306b\u3001\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u53ce\u675f\u3082\u767a\u6563\u3082\u3057\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\\(\\displaystyle \\lim_{ n \\to \\infty } (-1)^n\\)\u306e\u5834\u5408\u3001\\(1\\)\u3068\\(-1\\)\u3092\u7e70\u308a\u8fd4\u3059\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u300c\u6570\u5217\u306f\u632f\u52d5\u3059\u308b\u300d\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n \u305d\u308c\u3067\u306f\u3001\u5206\u6570\u5f0f\u3084\u7121\u7406\u5f0f\u3001\u6570\u5217\u306e\u548c\u306b\u3064\u3044\u3066\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u65b9\u6cd5\u306f\u3069\u308c\u3082\u5171\u901a\u3057\u3066\u304a\u308a\u3001\u6700\u3082\u5927\u304d\u3044\\(n\\)\u306e\u6b21\u6570\u3092\u7528\u3044\u3066\u5272\u3063\u305f\u308a\u3001\u5206\u6bcd\u306e\u6709\u5229\u5316\u3092\u3057\u305f\u308a\u3057\u30660\u306b\u53ce\u675f\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \u7b2c\\(n\\)\u9805\u304c\u4ee5\u4e0b\u306e\u5f0f\u3067\u3042\u308b\u5834\u5408\u3001\u6570\u5217\u306e\u6975\u9650\u306f\u3069\u306e\u3088\u3046\u306a\u5024\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n 1)<\/strong><\/p>\n \u6700\u3082\u5927\u304d\u3044\\(n\\)\u306e\u6b21\u6570\u3092\u5229\u7528\u3057\u3066\u5206\u6bcd\u3068\u5206\u5b50\u3092\u5272\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{3n^2+4n}{2n^2-1}\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{3+\\displaystyle\\frac{4}{n}}{2-\\displaystyle\\frac{1}{n^2}}\\)<\/p>\n \\(=\\displaystyle\\frac{3+0}{2+0}\\)<\/p>\n \\(=\\displaystyle\\frac{3}{2}\\)<\/p>\n 2)<\/strong><\/p>\n \u7121\u7406\u5f0f\u306b\u3064\u3044\u3066\u306f\u3001\u6700\u3082\u5927\u304d\u3044\u6b21\u6570\u3092\u5229\u7528\u3057\u3066\u5272\u308a\u7b97\u3092\u3057\u305f\u308a\u3001\u6709\u5229\u5316\u3092\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(\\displaystyle \\lim_{ n \\to \\infty } (\\sqrt{n^2+2n}-n)\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{n^2+2n-n^2}{\\sqrt{n^2+2n}+n}\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{2n}{\\sqrt{n^2+2n}+n}\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{2}{\\sqrt{1+\\displaystyle\\frac{2}{n}}+1}\\)<\/p>\n \\(=\\displaystyle\\frac{2}{\\sqrt{1+0}+1}\\)<\/p>\n \\(=1\\)<\/p>\n \u6b21\u306b\u3001\u6570\u5217\u306e\u548c\u306b\u3064\u3044\u3066\u7121\u9650\u6570\u5217\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u5f0f\u306b\u3064\u3044\u3066\u3001\u6975\u9650\u306e\u5024\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n \u516c\u5f0f\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{2+5+…+3n-1}{1+3+…+2n-1}\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{\\displaystyle\\sum_{k=1}^{n}{(3k-1)}}{\\displaystyle\\sum_{k=1}^{n}{(2k-1)}}\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{\\displaystyle\\frac{3}{2}n(n+1)-n}{n(n+1)-n}\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{\\displaystyle\\frac{3}{2}n^2+\\displaystyle\\frac{1}{2}n}{n^2}\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } \\left(\\displaystyle\\frac{3}{2}+\\displaystyle\\frac{1}{2n}\\right)\\)<\/p>\n \\(=\\displaystyle\\frac{3}{2}\\)<\/p>\n \u3053\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n \u305d\u308c\u3067\u306f\u3001\u6975\u9650\u306e\u6761\u4ef6\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u6570\u5217\u3092\u6c7a\u5b9a\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u3053\u3053\u307e\u3067\u89e3\u8aac\u3057\u305f\u3088\u3046\u306b\u3001\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n \u6761\u4ef6\u5f0f\u3092\u5229\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3057\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(\\displaystyle \\lim_{ n \\to \\infty } na_n\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } (3n-2)a_n\u00d7\\displaystyle\\frac{n}{3n-2}\\)<\/p>\n \\(=\\displaystyle \\lim_{ n \\to \\infty } (3n-2)a_n\u00d7\\displaystyle\\frac{1}{3-\\displaystyle\\frac{2}{n}}\\)<\/p>\n \\(=4\u00d7\\displaystyle\\frac{1}{3-0}\\)<\/p>\n \\(=\\displaystyle\\frac{4}{3}\\)<\/p>\n \u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u3053\u3053\u307e\u3067\u3001\u5f0f\u3092\u76f4\u63a5\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u305f\u3060\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u76f4\u63a5\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u3089\u308c\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u4e8c\u3064\u306e\u6570\u5217\u3092\u5229\u7528\u3057\u3066\u4e21\u5074\u3092\u631f\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n \u4f8b\u3048\u3070\\(\\displaystyle \\lim_{ n \\to \\infty } a_n\\)\u306b\u3064\u3044\u3066\u3001\\(0<\\displaystyle \\lim_{ n \\to \\infty } a_n<0\\)\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308c\u3070\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } a_n=0\\)\u3068\u306a\u308a\u307e\u3059\u3002<\/span>\u3053\u308c\u304c\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3067\u3059\u3002<\/p>\n \u305d\u308c\u3067\u306f\u3001\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3092\u5229\u7528\u3057\u3066\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u5f0f\u306b\u3064\u3044\u3066\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } a_n\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(\\displaystyle \\lim_{ n \\to \\infty } a_n\\)\u3092\u76f4\u63a5\u8a08\u7b97\u3059\u308b\u306e\u306f\u96e3\u3057\u3044\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u4e0d\u7b49\u53f7\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(a_n=\\displaystyle\\frac{1}{n^2+1}+\\displaystyle\\frac{1}{n^2+2}+…+\\displaystyle\\frac{1}{n^2+n}\\)\\(<\\displaystyle\\frac{1}{n^2}+\\displaystyle\\frac{1}{n^2}+…+\\displaystyle\\frac{1}{n^2}\\)<\/p>\n \u5206\u6bcd\u304c\u5c0f\u3055\u3044\u5834\u5408\u3001\u5024\u306f\u5927\u304d\u304f\u306a\u308b\u305f\u3081\u3001\u3053\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4e0d\u7b49\u53f7\u306e\u53f3\u5074\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(\\displaystyle\\frac{1}{n^2}+\\displaystyle\\frac{1}{n^2}+…+\\displaystyle\\frac{1}{n^2}\\)<\/p>\n \\(=\\displaystyle\\frac{1}{n^2}\u00d7n\\)<\/p>\n \\(=\\displaystyle\\frac{1}{n}\\)<\/p>\n \u307e\u305f\u3001\\(n\\)\u306f\u6b63\u306e\u6574\u6570\u306a\u306e\u3067\\(0<a_n\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n \u306a\u304a\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{1}{n}=0\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } a_n=0\\)\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3068\u540c\u3058\u3088\u3046\u306b\u3001\u4e0d\u7b49\u53f7\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u308b\u307b\u304b\u306e\u65b9\u6cd5\u306b\u8ffd\u3044\u51fa\u3057\u306e\u539f\u7406<\/span>\u304c\u3042\u308a\u307e\u3059\u3002\u7b54\u3048\u304c\u6b63\u306e\u7121\u9650\u5927\u3001\u307e\u305f\u306f\u8ca0\u306e\u7121\u9650\u5927\u3067\u3042\u308b\u3068\u304d\u306b\u8ffd\u3044\u51fa\u3057\u306e\u539f\u7406\u3092\u5229\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n \u4f8b\u3048\u3070\\(\\displaystyle \\lim_{ n \\to \\infty } a_n\\)\u3092\u8abf\u3079\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u3068\u304d\\(a_n>b_n\\)\u3067\u3042\u308a\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } b_n=\u221e\\)\u3067\u3042\u308b\u306a\u3089\u3001\u5f53\u7136\u306a\u304c\u3089\\(\\displaystyle \\lim_{ n \\to \\infty } a_n=\u221e\\)\u3067\u3059\u3002\u3053\u308c\u304c\u8ffd\u3044\u51fa\u3057\u306e\u539f\u7406\u3067\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n \\(0<sin\\displaystyle\\frac{\u03c0}{5}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n \u306a\u304a\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } \\sqrt{n}=\u221e\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } \\left(\\sqrt{n}+sin\\displaystyle\\frac{\u03c0}{5}\\right)=\u221e\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u8ffd\u3044\u51fa\u3057\u306e\u539f\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u306a\u304a\u3001\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u306b\u4e8c\u9805\u5b9a\u7406\u3092\u7528\u3044\u308b\u3068\u8a08\u7b97\u3067\u304d\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u6307\u6570\u578b\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u4e8c\u9805\u5b9a\u7406\u3092\u5229\u7528\u3067\u304d\u306a\u3044\u304b\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002\u5fa9\u7fd2\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u304c\u4e8c\u9805\u5b9a\u7406\u306e\u516c\u5f0f\u3067\u3059\u3002<\/p>\n \\((a+b)^n\\)<\/p>\n \\(=_nC_0a^n+_nC_1a^{n-1}b+_nC_2a^{n-2}b^2…\\)\\(+_nC_ra^{n-r}b^r+…\\)\\(+_nC_nb^n\\)<\/p>\n \u305d\u308c\u3067\u306f\u3001\u4e8c\u9805\u5b9a\u7406\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(2^n=(1+1)^n\\)\u3068\u8003\u3048\u3066\u3001\u4e8c\u9805\u5b9a\u7406\u3092\u7528\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5c55\u958b\u3057\u307e\u3059\u3002<\/p>\n \\((1+1)^n\\)<\/p>\n \\(=1+_nC_1+_nC_2+_nC_3+…\\)<\/p>\n \\(=1+n+\\displaystyle\\frac{n(n-1)}{2}\\)\\(+\\displaystyle\\frac{n(n-1)(n-2)}{6}\\)\\(+…\\)<\/p>\n \u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n \\(2^n>1+n+\\displaystyle\\frac{n(n-1)}{2}\\)\\(+\\displaystyle\\frac{n(n-1)(n-2)}{6}\\)<\/p>\n \\(2^n>\\displaystyle\\frac{n^3+5n+6}{6}\\)<\/p>\n \u3053\u3046\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n \\(2^n>\\displaystyle\\frac{n^3+5n+6}{6}\\)\\(>\\displaystyle\\frac{n^3}{6}\\)<\/p>\n \u4e8c\u9805\u5b9a\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\\(2^n>\\displaystyle\\frac{n^3}{6}\\)\u3092\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n \\(2^n>\\displaystyle\\frac{n^3}{6}\\)<\/p>\n \\(\\displaystyle\\frac{1}{2^n}<\\displaystyle\\frac{6}{n^3}\\)<\/p>\n \\(\\displaystyle\\frac{n^2}{2^n}<\\displaystyle\\frac{6}{n}\\)<\/p>\n \u307e\u305f\u3001\\(n\\)\u306f\u6574\u6570\u306a\u306e\u3067\\(0<\\displaystyle\\frac{n^2}{2^n}\\)\u3067\u3059\u3002<\/p>\n \u306a\u304a\\(\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{6}{n}=0\\)\u3067\u3042\u308b\u305f\u3081\u3001\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3088\u308a\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{n^2}{2^n}=0\\)\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n \u6570\u5217\u306e\u8a08\u7b97\u3067\u306f\u3001\u672b\u9805\u304c\u5b58\u5728\u3057\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u7121\u9650\u6570\u5217\u306e\u8a08\u7b97\u3092\u884c\u3048\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n \u7121\u9650\u6570\u5217\u3067\u306f\u7279\u5b9a\u306e\u5024\u306b\u53ce\u675f\u3057\u305f\u308a\u3001\u767a\u6563\u306b\u3088\u3063\u3066\u5024\u304c\u7121\u9650\u5927\u306b\u306a\u3063\u305f\u308a\u3057\u307e\u3059\u3002\u76f4\u611f\u3067\u306f\u7b54\u3048\u304c\u308f\u304b\u3089\u306a\u3044\u305f\u3081\u3001\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n \u306a\u304a\u3001\u6975\u9650\u3092\u76f4\u63a5\u8a08\u7b97\u3067\u304d\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3084\u8ffd\u3044\u51fa\u3057\u306e\u539f\u7406\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u4e8c\u9805\u5b9a\u7406\u3068\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6975\u9650\u306e\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u30b1\u30fc\u30b9\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n \u7121\u9650\u6570\u5217\u3067\u7b54\u3048\u3092\u5f97\u308b\u65b9\u6cd5\u306f\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u6570\u5217\u306e\u6975\u9650\u306b\u95a2\u3059\u308b\u554f\u984c\u3092\u89e3\u3051\u3070\u3044\u3044\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u6570\u5217\u306e\u8a08\u7b97\u3092\u3059\u308b\u969b\u3001\\(n\\)\u306e\u5024\u3092\u7121\u9650\u5927\u306b\u5927\u304d\u304f\u3059\u308b\u3068\u304d\u306b\u3069\u306e\u3088\u3046\u306a\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u3053\u3046\u3057\u305f\u6570\u5217\u3092\u7121\u9650\u6570\u5217\u3068\u3044\u3044\u307e\u3059\u3002 \u7121\u9650\u6570\u5217\u3067\u3069\u306e\u3088\u3046\u306a\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u306e\u304b\u76f4\u611f\u3067\u5224\u65ad\u3059\u308b\u306e\u306f\u96e3\u3057\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u6570\u5217\u306e […]<\/p>\n","protected":false},"author":1,"featured_media":12637,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-12629","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-h-math"},"_links":{"self":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12629","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/comments?post=12629"}],"version-history":[{"count":13,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12629\/revisions"}],"predecessor-version":[{"id":12702,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12629\/revisions\/12702"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/12637"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=12629"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=12629"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=12629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\u5206\u6570\u5f0f\u3001\u7121\u7406\u5f0f\u3001\u6570\u5217\u306e\u548c\u306e\u8a08\u7b97<\/h3>\n
\n
\n
\u6975\u9650\u306e\u6761\u4ef6\u3092\u5229\u7528\u3057\u3066\u6570\u5217\u3092\u6c7a\u5b9a\u3059\u308b<\/h3>\n
\n
\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\uff1a\u4e0d\u7b49\u5f0f\u306e\u5229\u7528<\/h2>\n
\n
\n
\u8ffd\u3044\u51fa\u3057\u306e\u539f\u7406\uff1a\u7b54\u3048\u304c\u7121\u9650\u5927\u306e\u3068\u304d\u306b\u5229\u7528<\/h3>\n
\n
\n
\u4e8c\u9805\u5b9a\u7406\u3092\u7528\u3044\u308b\u6307\u6570\u578b\u306e\u6975\u9650\u306e\u8a08\u7b97<\/h3>\n
\n
\n
\u7121\u9650\u6570\u5217\u3067\u306e\u7b54\u3048\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u3059\u308b<\/h2>\n