{"id":12640,"date":"2023-02-08T17:00:52","date_gmt":"2023-02-08T08:00:52","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=12640"},"modified":"2023-02-14T10:37:02","modified_gmt":"2023-02-14T01:37:02","slug":"sequence-7","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/sequence-7.html","title":{"rendered":"\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u6975\u9650\uff1a\u53ce\u675f\u6761\u4ef6\u3068\u6f38\u5316\u5f0f\u30fb\u4e0d\u7b49\u5f0f\u306e\u5229\u7528"},"content":{"rendered":"\n<p>\u7b49\u6bd4\u6570\u5217\u306b\u95a2\u3059\u308b\u7121\u9650\u6570\u5217\u3092\u7121\u9650\u7b49\u6bd4\u6570\u5217\u3068\u3044\u3044\u307e\u3059\u3002\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u516c\u6bd4\\(r\\)\u306b\u3088\u3063\u3066\u5024\u304c\u53ce\u675f\u3059\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u767a\u6563\u3059\u308b\u306e\u304b\u304c\u5909\u308f\u308a\u307e\u3059\u3002<\/p>\n<p>\u7121\u9650\u7b49\u6bd4\u6570\u5217\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u306b\u3088\u308a\u30010\u306b\u306a\u308b\u5024\u3084\u7121\u9650\u5927\u306b\u306a\u308b\u5024\u3092\u78ba\u8a8d\u3059\u308b\u306e\u3067\u3059\u3002\u76f4\u611f\u3067\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u5272\u308a\u7b97\u3084\u5834\u5408\u5206\u3051\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u8a08\u7b97\u3067\u306f\u3001\u6f38\u5316\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u6f38\u5316\u5f0f\u306e\u8a08\u7b97\u3092\u3057\u305f\u5f8c\u3001\u6570\u5217\u306e\u6975\u9650\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002\u306a\u304a\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u8a08\u7b97\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u8a08\u7b97\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u516c\u6bd4\\(r\\)\u306b\u3088\u3063\u3066\u5909\u5316\u3059\u308b\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u6975\u9650<\/h2>\n<p>\u7121\u9650\u7b49\u6bd4\u6570\u5217\u3067\u5f97\u3089\u308c\u308b\u7b54\u3048\u306f\u516c\u6bd4\\(r\\)\u306b\u3088\u3063\u3066\u5909\u5316\u3057\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u7121\u9650\u7b49\u6bd4\u6570\u5217\\(r^n\\)\u306e\u6975\u9650\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(r&gt;1\\)\u306e\u5834\u5408\uff1a\\(\\displaystyle \\lim_{ n \\to \\infty } r^n=\u221e\\)<\/li>\n<li>\\(r=1\\)\u306e\u5834\u5408\uff1a\\(\\displaystyle \\lim_{ n \\to \\infty } r^n=1\\)<\/li>\n<li>\\(|r|&lt;1\\)\u306e\u5834\u5408\uff1a\\(\\displaystyle \\lim_{ n \\to \\infty } r^n=0\\)<\/li>\n<li>\\(r\u2266-1\\)\u306e\u5834\u5408\uff1a\\(\\displaystyle \\lim_{ n \\to \\infty } r^n\\)\u306f\u632f\u52d5\u3059\u308b<\/li>\n<\/ul>\n<p>\\(r&gt;1\\)\u306e\u5834\u5408\u306e\u5834\u5408\u3001\u5f53\u7136\u306a\u304c\u3089\u7121\u9650\u5927\u306b\u5024\u306f\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002\u307e\u305f\\(\\displaystyle \\lim_{ n \\to \\infty } 1^n=1\\)\u3068\u306a\u308a\u307e\u3059\u3057\u3001\\(|r|&lt;1\\)\u3067\\(\\displaystyle \\lim_{ n \\to \\infty } r^n=0\\)\u3068\u306a\u308b\u306e\u306f\u8aac\u660e\u3057\u306a\u304f\u3066\u3082\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3067\\(r\u2266-1\\)\u306e\u5834\u5408\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } r^n\\)\u306f\u632f\u52d5\u3057\u307e\u3059\u3002\\(r&lt;-1\\)\u3067\u306f\u5024\u304c\u7121\u9650\u5927\u306b\u5927\u304d\u304f\u306a\u308b\u3082\u306e\u306e\u3001\u6b63\u306e\u7121\u9650\u5927\u3068\u8ca0\u306e\u7121\u9650\u5927\u304c\u4ea4\u4e92\u306b\u73fe\u308c\u308b\u305f\u3081\u3001\u3053\u306e\u5834\u5408\u306f\u6975\u9650\u304c\u5b58\u5728\u3057\u306a\u3044\u3068\u8003\u3048\u307e\u3059\u3002<\/p>\n<h3>\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5b9f\u969b\u306b\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u6975\u9650\u306b\u95a2\u3059\u308b\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u5f0f\u306e\u6975\u9650\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(5^n-2^n\\)<\/li>\n<\/ul>\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\lim_{ n \\to \\infty } (5^n-2^n)\\)<\/p>\n<p>\\(=\\displaystyle \\lim_{ n \\to \\infty } 5^n\\left\\{1-\\left(\\displaystyle\\frac{2}{5}\\right)^n\\right\\}\\)<\/p>\n<p>\\(=\u221e(1-0)\\)<\/p>\n<p>\\(=\u221e\\)<\/p>\n<p>\u307e\u305f\u3001\u6b21\u306e\u5f0f\u306e\u6975\u9650\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{5^{n+1}-3^n}{5^n-4^n}\\)<\/li>\n<\/ul>\n<p>\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{5^{n+1}-3^n}{5^n-4^n}\\)<\/p>\n<p>\\(=\\displaystyle \\lim_{ n \\to \\infty } \\displaystyle\\frac{5-\\displaystyle\\frac{3^n}{5^n}}{1-\\displaystyle\\frac{4^n}{5^n}}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{5-0}{1-0}\\)<\/p>\n<p>\\(=5\\)<\/p>\n<p>\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<h3>\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u53ce\u675f\u6761\u4ef6<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u6761\u4ef6\u3092\u7528\u3044\u3066\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u53ce\u675f\u6761\u4ef6\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u5f0f\u306b\u3064\u3044\u3066\u3001\u53ce\u675f\u3059\u308b\u3088\u3046\u306b\\(x\\)\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\left(\\displaystyle\\frac{3x}{x^2+2}\\right)^n\\)<\/li>\n<\/ul>\n<p>\u53ce\u675f\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(-1&lt;\\displaystyle\\frac{3x}{x^2+2}\u22661\\)<\/li>\n<\/ul>\n<p>\\(-1&lt;\\displaystyle\\frac{3x}{x^2+2}\\)\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(-1&lt;\\displaystyle\\frac{3x}{x^2+2}\\)<\/p>\n<p>\\(x^2+3x+2&gt;0\\)<\/p>\n<p>\\((x+2)(x+1)&gt;0\\)<\/p>\n<p>\\(x&lt;-2,-1&lt;x\\) &#8211; \u2460<\/p>\n<p>\u307e\u305f\\(\\displaystyle\\frac{3x}{x^2+2}\u22661\\)\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{3x}{x^2+2}\u22661\\)<\/p>\n<p>\\(0\u2266x^2-3x+2\\)<\/p>\n<p>\\(0\u2266(x-1)(x-2)\\)<\/p>\n<p>\\(x\u22661,2\u2266x\\) &#8211; \u2461<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/02\/few1.jpg\" alt=\"\" width=\"431\" height=\"124\" class=\"aligncenter size-full wp-image-12644\" \/><\/p>\n<p>\u2460\u304b\u3064\u2461\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u7b54\u3048\u306f\\(x&lt;-2\\)\u3001\\(-1&lt;x\u22661\\)\u3001\\(2\u2266x\\)\u3068\u306a\u308a\u307e\u3059\u3002\u6761\u4ef6\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2>\u96a3\u63a52\u9805\u9593\u306e\u6f38\u5316\u5f0f\u3068\u6975\u9650<\/h2>\n<p>\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u8a08\u7b97\u3067\u306f\u3001\u6f38\u5316\u5f0f\u304c\u95a2\u308f\u308b\u554f\u984c\u3092\u89e3\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u6f38\u5316\u5f0f\u3068\u6975\u9650\u306b\u3064\u3044\u3066\u3001\u6f38\u5316\u5f0f\u3092\u5229\u7528\u3057\u3066\u4e00\u822c\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u3001\u5bb9\u6613\u306b\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(a_1=1\\)\u3001\\(a_{n+1}=3a_n+4\\)\u3068\u306a\u308b\u6570\u5217\\(\\{a_n\\}\\)\u306e\u6975\u9650\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\\(\u03b1=3\u03b1+4\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(\u03b1=-2\\)\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(a_{n+1}-\u03b1=3(a_n-\u03b1)\\)<\/p>\n<p>\\(a_{n+1}+2=3(a_n+2)\\)<\/p>\n<p>\u6570\u5217\\(\\{a_n+2\\}\\)\u306f\u521d\u9805\\(a_1+2=3\\)\u3001\u516c\u6bd43\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(a_n+2=3^n\\)<\/p>\n<p>\\(a_n=3^n-2\\)<\/p>\n<p>\u6b21\u306b\u3001\u3053\u306e\u6570\u5217\u306e\u6975\u9650\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle \\lim_{ n \\to \\infty } (3^n-2)\\)<\/p>\n<p>\\(=\u221e\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u6f38\u5316\u5f0f\u3068\u6975\u9650\u306b\u95a2\u3059\u308b\u554f\u984c\u306b\u3064\u3044\u3066\u3001\u6f38\u5316\u5f0f\u3092\u5229\u7528\u3057\u3066\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3059\u308c\u3070\u3001\u5bb9\u6613\u306b\u7b54\u3048\u3092\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<h3>\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3092\u5229\u7528\u3059\u308b\u6f38\u5316\u5f0f\u3068\u6975\u9650<\/h3>\n<p>\u306a\u304a\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u6975\u9650\u3067\u5b66\u3076\u5185\u5bb9\u3092\u5229\u7528\u3057\u3066\u6f38\u5316\u5f0f\u306b\u95a2\u3059\u308b\u554f\u984c\u3092\u89e3\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(a_1=1\\)\u3001\\(a_{n+1}=\\displaystyle\\frac{1}{2}\\left(a_n+\\displaystyle\\frac{1}{25a_n}\\right)\\)\u3068\u306a\u308b\u6570\u5217\\(\\{a_n\\}\\)\u304c\u3042\u308a\u307e\u3059\u3002<\/li>\n<\/ul>\n<ol>\n<li>\\(a_n&gt;\\displaystyle\\frac{1}{5}\\)\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<li>\\(a_{n+1}-\\displaystyle\\frac{1}{5}&lt;\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)\\)\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/li>\n<li>\\(\\displaystyle \\lim_{ n \\to \\infty } a_n\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ol>\n<p>\u6570\u5217\\(\\{a_n\\}\\)\u306e\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3059\u308b\u306e\u306f\u96e3\u3057\u3044\u305f\u3081\u3001\u307b\u304b\u306e\u65b9\u6cd5\u306b\u3088\u3063\u3066\u6f38\u5316\u5f0f\u306e\u6975\u9650\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>1) \\(a_n&gt;\\displaystyle\\frac{1}{5}\\)\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046<\/strong><\/p>\n<p>\u6f38\u5316\u5f0f\u304c\u95a2\u308f\u308b\u8a3c\u660e\u3067\u306f\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u3092\u5229\u7528\u3059\u308b\u3068\u3046\u307e\u304f\u3044\u304f\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><strong>\u30fb[1] \\(n=1\\)\u306e\u3068\u304d\u306b\u6210\u308a\u7acb\u3064\u3068\u8a3c\u660e\u3059\u308b<\/strong><\/p>\n<p>\\(n=1\\)\u306e\u3068\u304d\u3001\\(a_1=1\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(a_1&gt;\\displaystyle\\frac{1}{5}\\)\u3067\u3059\u3002<\/p>\n<p><strong>\u30fb[2] \\(n=k\\)\u306e\u3068\u304d\u306b\u6210\u308a\u7acb\u3064\u3068\u4eee\u5b9a\u3057\u3001\\(n=k+1\\)\u3067\u3042\u3063\u3066\u3082\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b<\/strong><\/p>\n<p>\\(n=k\\)\u306e\u3068\u304d\u3001\\(a_k&gt;\\displaystyle\\frac{1}{5}\\)\u304c\u6210\u308a\u7acb\u3064\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002\u306a\u304a\\(n=k+1\\)\u306e\u3068\u304d\u3001\u3064\u307e\u308a\\(a_{k+1}&gt;\\displaystyle\\frac{1}{5}\\)\u304c\u6210\u308a\u7acb\u3064\u3068\u8a3c\u660e\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\\(a_{k+1}-\\displaystyle\\frac{1}{5}&gt;0\\)\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u3053\u3067\u3001\\(a_{k+1}=\\displaystyle\\frac{1}{2}\\left(a_k+\\displaystyle\\frac{1}{25a_k}\\right)\\)\u3092\u5229\u7528\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a_{k+1}=\\displaystyle\\frac{1}{2}\\left(a_k+\\displaystyle\\frac{1}{25a_k}\\right)\\)<\/p>\n<p>\\(a_{k+1}-\\displaystyle\\frac{1}{5}=\\displaystyle\\frac{1}{2}\\left(a_k+\\displaystyle\\frac{1}{25a_k}\\right)-\\displaystyle\\frac{1}{5}\\)<\/p>\n<p>\\(a_{k+1}-\\displaystyle\\frac{1}{5}=\\displaystyle\\frac{1}{50a_k}(25a_k^2+1-10a_k)\\)<\/p>\n<p>\\(a_{k+1}-\\displaystyle\\frac{1}{5}=\\displaystyle\\frac{1}{50a_k}(5a_k-1)^2\\)<\/p>\n<p>\\(a_k&gt;\\displaystyle\\frac{1}{5}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(a_{k+1}-\\displaystyle\\frac{1}{5}&gt;0\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(a_{k+1}&gt;\\displaystyle\\frac{1}{5}\\)\u3068\u306a\u308a\u307e\u3059\u3002[1]\u3068[2]\u3088\u308a\u3001\u3059\u3079\u3066\u306e\u81ea\u7136\u6570\\(n\\)\u3067\\(a_n&gt;\\displaystyle\\frac{1}{5}\\)\u306b\u306a\u308b\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p><strong>2) \\(a_{n+1}-\\displaystyle\\frac{1}{5}&lt;\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)\\)\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/strong><\/p>\n<p>\u53f3\u8fba\u304b\u3089\u5de6\u8fba\u3092\u5f15\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)-a_{n+1}+\\displaystyle\\frac{1}{5}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)\\)\\(-\\displaystyle\\frac{1}{2}\\left(a_n+\\displaystyle\\frac{1}{25a_n}\\right)\\)\\(+\\displaystyle\\frac{1}{5}\\)<\/p>\n<p>\\(=\\displaystyle\\frac{1}{10}-\\displaystyle\\frac{1}{50a_n}\\)<\/p>\n<p>\\(a_n&gt;\\displaystyle\\frac{1}{5}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(\\displaystyle\\frac{1}{10}-\\displaystyle\\frac{1}{50a_n}&gt;0\\)\u3067\u3059\u3002\u3053\u3046\u3057\u3066\u3001\\(a_{n+1}-\\displaystyle\\frac{1}{5}&lt;\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)\\)\u3092\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<p><strong>3) \\(\\displaystyle \\lim_{ n \\to \\infty } a_n\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046<\/strong><\/p>\n<p>\u554f\u984c1\u3068\u554f\u984c2\u3088\u308a\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(0&lt;a_{n+1}-\\displaystyle\\frac{1}{5}&lt;\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\\(a_{n+1}-\\displaystyle\\frac{1}{5}&lt;\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)\\)\u306b\u3064\u3044\u3066\u3001\u4e0d\u7b49\u53f7\u3092\u7b49\u53f7\u306b\u5909\u3048\u3066\u6f38\u5316\u5f0f\u306e\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a_{n+1}-\\displaystyle\\frac{1}{5}=\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)\\)\u306b\u3064\u3044\u3066\u3001\u6570\u5217\\(\\left\\{a_n-\\displaystyle\\frac{1}{5}\\right\\}\\)\u306f\u521d\u9805\\(1-\\displaystyle\\frac{1}{5}=\\displaystyle\\frac{4}{5}\\)\u3001\u516c\u6bd4\\(\\displaystyle\\frac{1}{2}\\)\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n}-\\displaystyle\\frac{1}{5}=\\left(\\displaystyle\\frac{1}{2}\\right)^{n-1}\u00b7\\displaystyle\\frac{4}{5}\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u8a08\u7b97\u3088\u308a\u3001\\(\\displaystyle\\frac{1}{2}\\left(a_n-\\displaystyle\\frac{1}{5}\\right)\\)\\(=\\left(\\displaystyle\\frac{1}{2}\\right)^{n}\u00b7\\displaystyle\\frac{4}{5}\\)\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u7b49\u53f7\u3092\u4e0d\u7b49\u53f7\u306b\u623b\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n}-\\displaystyle\\frac{1}{5}&lt;\\left(\\displaystyle\\frac{1}{2}\\right)^{n}\u00b7\\displaystyle\\frac{4}{5}\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\\(\\displaystyle \\lim_{ n \\to \\infty } \\left(\\displaystyle\\frac{1}{2}\\right)^{n}\u00b7\\displaystyle\\frac{4}{5}=0\\)\u3067\u3042\u308b\u305f\u3081\u3001\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3088\u308a\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } \\left(a_{n}-\\displaystyle\\frac{1}{5}\\right)=0\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(\\displaystyle \\lim_{ n \\to \\infty } a_n=\\displaystyle\\frac{1}{5}\\)\u3067\u3059\u3002<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5f0f\u306e\u5909\u63db\u3068\u306f\u3055\u307f\u3046\u3061\u306e\u539f\u7406\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306a\u304f\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u6027\u8cea\u3068\u6f38\u5316\u5f0f\u306e\u95a2\u4fc2\u3092\u5b66\u3076<\/h2>\n<p>\u7121\u9650\u7b49\u6bd4\u6570\u5217\u3067\u91cd\u8981\u306a\u306e\u306f\u516c\u6bd4\\(r\\)\u3067\u3059\u3002\u516c\u6bd4\u306e\u5024\u306b\u3088\u3063\u3066\u3001\u6570\u5217\u306e\u6975\u9650\u304c\u53ce\u675f\u3059\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u767a\u6563\u3059\u308b\u306e\u304b\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u632f\u52d5\u3059\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002\u304b\u3063\u3053\u3092\u5229\u7528\u3057\u3066\u5206\u6570\u3092\u4f5c\u3063\u305f\u308a\u3001\u5272\u308a\u7b97\u3092\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5024\u304c\u53ce\u675f\u3059\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u767a\u6563\u3059\u308b\u306e\u304b\u78ba\u8a8d\u3059\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u307e\u305f\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u8a08\u7b97\u3067\u306f\u3001\u6f38\u5316\u5f0f\u3092\u542b\u3080\u554f\u984c\u3092\u89e3\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u6f38\u5316\u5f0f\u3092\u5229\u7528\u3057\u3066\u4e00\u822c\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308c\u3070\u3001\u6570\u5217\u306e\u6975\u9650\u306e\u8a08\u7b97\u306f\u5bb9\u6613\u3067\u3059\u3002\u305f\u3060\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u4e00\u822c\u9805\u3092\u5f97\u308b\u306e\u304c\u96e3\u3057\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u5834\u5408\u306f\u4e00\u822c\u9805\u3092\u8a08\u7b97\u305b\u305a\u306b\u7b54\u3048\u3092\u5f97\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u7121\u9650\u7b49\u6bd4\u6570\u5217\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u554f\u984c\u306e\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7b49\u6bd4\u6570\u5217\u306b\u95a2\u3059\u308b\u7121\u9650\u6570\u5217\u3092\u7121\u9650\u7b49\u6bd4\u6570\u5217\u3068\u3044\u3044\u307e\u3059\u3002\u7121\u9650\u7b49\u6bd4\u6570\u5217\u306e\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u516c\u6bd4\\(r\\)\u306b\u3088\u3063\u3066\u5024\u304c\u53ce\u675f\u3059\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u767a\u6563\u3059\u308b\u306e\u304b\u304c\u5909\u308f\u308a\u307e\u3059\u3002 \u7121\u9650\u7b49\u6bd4\u6570\u5217\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u306b\u3088\u308a\u3001 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":12652,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-12640","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\/12640","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=12640"}],"version-history":[{"count":14,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12640\/revisions"}],"predecessor-version":[{"id":12725,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12640\/revisions\/12725"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/12652"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=12640"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=12640"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=12640"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}