{"id":12133,"date":"2023-01-08T17:20:32","date_gmt":"2023-01-08T08:20:32","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=12133"},"modified":"2023-01-11T15:17:25","modified_gmt":"2023-01-11T06:17:25","slug":"recurrence-relation-4","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/recurrence-relation-4.html","title":{"rendered":"\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\uff1a\u9006\u6570\u3084\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u89e3\u304d\u65b9"},"content":{"rendered":"\n<p>\u6570\u5b66\u306e\u4e2d\u3067\u3082\u3001\u5b8c\u5168\u306a\u308b\u6697\u8a18\u79d1\u76ee\u3068\u306a\u308b\u306e\u304c\u6f38\u5316\u5f0f\u3067\u3059\u3002\u89e3\u304d\u65b9\u3092\u899a\u3048\u3066\u3044\u308c\u3070\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3082\u306e\u306e\u3001\u89e3\u304d\u65b9\u3092\u899a\u3048\u3066\u3044\u306a\u3051\u308c\u3070\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3082\u540c\u69d8\u3067\u3059\u3002<\/p>\n<p>\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3067\u306f\u9006\u6570\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305f\u3060\u3001\u5358\u306b\u9006\u6570\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3067\u306f\u3001\u89e3\u304d\u65b9\u306b2\u3064\u306e\u30d1\u30bf\u30fc\u30f3\u304c\u3042\u308a\u307e\u3059\u3002\u7b54\u3048\u3092\u5f97\u308b\u305f\u3081\u306b\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u89e3\u304d\u65b9\u3092\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306b\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3092\u89e3\u3051\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u9006\u6570\u3084\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u4e00\u822c\u9805\u3092\u5f97\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u9006\u6570\u3092\u5229\u7528\u3057\u3066\u6570\u5217\u306e\u554f\u984c\u3092\u89e3\u304f\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f<\/h2>\n<p>\u9006\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3067\u6700\u3082\u5358\u7d14\u306a\u306e\u306f\u3001\u5206\u5b50\u306b\\(a_n\\)\u306e\u307f\u304c\u5b58\u5728\u3059\u308b\u30b1\u30fc\u30b9\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001<span style=\"color: #0000ff;\">\u9006\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5bb9\u6613\u306b\u4e00\u822c\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p>\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(a_1=1\\)\u3001\\(a_{n+1}=\\displaystyle\\frac{a_n}{2a_n+1}\\)\u306b\u3088\u3063\u3066\u5b9a\u3081\u3089\u308c\u308b\u6570\u5217\\(\\{a_n\\}\\)\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u554f\u984c\u6587\u306e\u6f38\u5316\u5f0f\u3067\u306f\u3001\u5206\u5b50\u306b\u542b\u307e\u308c\u308b\u8981\u7d20\u306f\\(a_n\\)\u306e\u307f\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u9006\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(\\displaystyle\\frac{1}{a_{n+1}}=\\displaystyle\\frac{1}{a_n}+2\\)<\/li>\n<\/ul>\n<p>\u6570\u5217\\(\\left\\{\\displaystyle\\frac{1}{a_n}\\right\\}\\)\u3068\u3044\u3046\u306e\u306f\u3001\u521d\u9805\\(\\displaystyle\\frac{1}{a_1}=1\\)\u3001\u516c\u5dee2\u306e\u7b49\u5dee\u6570\u5217\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1}{a_n}=1+(n-1)2\\)<\/p>\n<p>\\(\\displaystyle\\frac{1}{a_n}=2n-1\\)<\/p>\n<p>\\(a_n=\\displaystyle\\frac{1}{2n-1}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u9006\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u306e\u89e3\u304d\u65b9\u3068\u7279\u6027\u65b9\u7a0b\u5f0f<\/h2>\n<p>\u305f\u3060\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3067\u306f\u3001\u9006\u6570\u3092\u5229\u7528\u3059\u308b\u3060\u3051\u3067\u306f\u7b54\u3048\u3092\u5f97\u3089\u308c\u306a\u3044\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3001\u5206\u5b50\u306b\\(a_n\\)\u3060\u3051\u3067\u306a\u304f\u3001\u8db3\u3057\u7b97\u307e\u305f\u306f\u5f15\u304d\u7b97\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u30b1\u30fc\u30b9\u304c\u8a72\u5f53\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+1}=\\displaystyle\\frac{a_n-9}{a_n-5}\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u5834\u5408\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3066\u6f38\u5316\u5f0f\u3092\u7b49\u5dee\u6570\u5217\u578b\u3001\u307e\u305f\u306f\u7b49\u6bd4\u6570\u5217\u578b\u3078\u5909\u5f62\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u3053\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e2\u7a2e\u985e\u306b\u5206\u3051\u3066\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u3082\u3064<\/li>\n<li>\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u7570\u306a\u308b2\u3064\u306e\u89e3\u3092\u3082\u3064<\/li>\n<\/ul>\n<p>\u89e3\u304d\u65b9\u304c\u7570\u306a\u308b\u305f\u3081\u3001\u305d\u308c\u305e\u308c\u306e\u65b9\u6cd5\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u3082\u3064\u30b1\u30fc\u30b9\u306e\u8a08\u7b97<\/h3>\n<p>\u6f38\u5316\u5f0f\u306f\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u4f8b\u984c\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u7b54\u3048\u306e\u5c0e\u51fa\u6cd5\u3092\u899a\u3048\u308b\u306e\u304c\u52b9\u7387\u7684\u3067\u3059\u3002\u305d\u3053\u3067\u4ee5\u4e0b\u306e\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u3082\u3064\u3068\u304d\u3001\u3069\u306e\u3088\u3046\u306b\u4e00\u822c\u9805\u3092\u5f97\u308c\u3070\u3044\u3044\u306e\u304b\u5b66\u3073\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(a_1=8\\)\u3001\\(a_{n+1}=\\displaystyle\\frac{a_n-9}{a_n-5}\\)\u306b\u3088\u3063\u3066\u5b9a\u3081\u3089\u308c\u308b\u6570\u5217\\(\\{a_n\\}\\)\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u3001\\(a_{n+1}=x\\)\u3001\\(a_n=x\\)\u3068\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002\u305d\u3053\u3067\u3001\\(a_{n+1}=\\displaystyle\\frac{a_n-9}{a_n-5}\\)\u3092\u5229\u7528\u3057\u3066\u4ee5\u4e0b\u306e\u8a08\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x=\\displaystyle\\frac{x-9}{x-5}\\)<\/p>\n<p>\\(x(x-5)=x-9\\)<\/p>\n<p>\\(x^2-6x+9=0\\)<\/p>\n<p>\\((x-3)^2=0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(x=3\\)\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u03b1\u3092\u3082\u3064\u5834\u5408\u3001\\(a_{n+1}=\\displaystyle\\frac{ra_n-s}{pa_n-q}\\)\u306b\u5bfe\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+1}-\u03b1=\\displaystyle\\frac{ra_n-s}{pa_n-q}-\u03b1\\)<\/li>\n<\/ul>\n<p>\u305d\u3053\u3067\u3001\\(a_{n+1}=\\displaystyle\\frac{a_n-9}{a_n-5}\\)\u3068\\(x=3\\)\u3092\u5229\u7528\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a_{n+1}-3=\\displaystyle\\frac{a_n-9}{a_n-5}-3\\)<\/p>\n<p>\\(a_{n+1}-3=\\displaystyle\\frac{a_n-9}{a_n-5}\\)\\(-\\displaystyle\\frac{3(a_n-5)}{a_n-5}\\)<\/p>\n<p>\\(a_{n+1}-3=\\displaystyle\\frac{-2a_n+6}{a_n-5}\\)<\/p>\n<p>\\(a_{n+1}-3=\\displaystyle\\frac{-2(a_n-3)}{a_n-5}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u6f38\u5316\u5f0f\u3092\u5909\u5f62\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h4>\u80cc\u7406\u6cd5\u3092\u5229\u7528\u3057\u3001\u9006\u6570\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u3089\u306a\u3044\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b<\/h4>\n<p>\u6b21\u306b\u3001\u9006\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1}{a_{n+1}-3}=\\displaystyle\\frac{a_n-5}{-2(a_n-3)}\\)<\/p>\n<p>\u305f\u3060\u9006\u6570\u3092\u5229\u7528\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u5206\u6bcd\u304c\u30bc\u30ed\u3060\u3068\u4e0d\u9069\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(a_n\u22603\\)\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u80cc\u7406\u6cd5\u3092\u5229\u7528\u3057\u3066\\(a_n\u22603\\)\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a_{n+1}=3\\)\u3068\u3059\u308b\u3068\u3001\\(a_{n+1}-3=0\\)\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(0=\\displaystyle\\frac{-2(a_n-3)}{a_n-5}\\)<\/p>\n<p>\\(0=-2(a_n-3)\\)<\/p>\n<p>\\(a_n=3\\)<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+1}=a_n=&#8230;\\)\\(=a_1=3\\)<\/li>\n<\/ul>\n<p>\u305f\u3060\\(a_1=8\\)\u3067\u3042\u308b\u305f\u3081\u3001\u77db\u76fe\u3057\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\\(a_n\u22603\\)\u3067\u3059\u3002<\/p>\n<h4>\u9006\u6570\u3092\u5229\u7528\u3057\u3066\u4e00\u822c\u9805\u3092\u5f97\u308b<\/h4>\n<p>\\(a_n\u22603\\)\u3092\u8a3c\u660e\u3067\u304d\u305f\u305f\u3081\u3001\u9006\u6570\u3092\u5229\u7528\u3067\u304d\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1}{a_{n+1}-3}=\\displaystyle\\frac{a_n-5}{-2(a_n-3)}\\)<\/p>\n<p>\\(\\displaystyle\\frac{1}{a_{n+1}-3}=\\displaystyle\\frac{(a_n-3)-2}{-2(a_n-3)}\\)<\/p>\n<p>\\(\\displaystyle\\frac{1}{a_{n+1}-3}=\\displaystyle\\frac{1}{a_n-3}\\)\\(-\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u6570\u5217\\(\\left\\{\\displaystyle\\frac{1}{a_n-3}\\right\\}\\)\u306f\u521d\u9805\\(\\displaystyle\\frac{1}{a_1-3}=\\displaystyle\\frac{1}{5}\\)\u3001\u516c\u5dee\\(-\\displaystyle\\frac{1}{2}\\)\u306e\u7b49\u5dee\u6570\u5217\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{1}{a_n-3}=\\displaystyle\\frac{1}{5}+(n-1)\u00b7-\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\\(\\displaystyle\\frac{1}{a_n-3}=\\displaystyle\\frac{7-5n}{10}\\)<\/p>\n<p>\\(a_n-3=\\displaystyle\\frac{10}{7-5n}\\)<\/p>\n<p>\\(a_n=\\displaystyle\\frac{10}{7-5n}+3\\)<\/p>\n<p>\\(a_n=\\displaystyle\\frac{31-15n}{7-5n}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u3082\u3064\u5834\u5408\u306b\u3064\u3044\u3066\u3001\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u306e\u4e00\u822c\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u7570\u306a\u308b2\u3064\u306e\u89e3\u3092\u3082\u3064\u5834\u5408\u306e\u89e3\u304d\u65b9<\/h3>\n<p>\u6b21\u306b\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u7570\u306a\u308b2\u3064\u306e\u89e3\u3092\u3082\u3064\u5834\u5408\u306e\u4e00\u822c\u9805\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u3067\u4e00\u822c\u9805\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u78ba\u8a8d\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_1=3\\)\u3001\\(a_{n+1}=\\displaystyle\\frac{4a_n-2}{a_n+1}\\)\u306b\u3088\u3063\u3066\u5b9a\u3081\u3089\u308c\u308b\u6570\u5217\\(\\{a_n\\}\\)\u306e\u4e00\u822c\u9805\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u5f97\u308b\u3068\u3044\u3046\u65b9\u91dd\u306f\u540c\u3058\u3067\u3059\u3002\u305d\u3053\u3067\\(a_{n+1}=x\\)\u3001\\(a_n=x\\)\u3068\u7f6e\u304d\u63db\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(x=\\displaystyle\\frac{4x-2}{x+1}\\)<\/p>\n<p>\\(x(x+1)=4x-2\\)<\/p>\n<p>\\(x^2-3x+2=0\\)<\/p>\n<p>\\((x-1)(x-2)=0\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\\(x=1,2\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002\u306a\u304a\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u03b1\u3068\u03b2\u3092\u89e3\u306b\u3082\u3064\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(b_n=\\displaystyle\\frac{a_n-\u03b1}{a_n-\u03b2}\\)<\/li>\n<\/ul>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u304c2\u3064\u306e\u89e3\u3092\u3082\u3064\u5834\u5408\u3001\u5fc5\u305a\u3053\u306e\u5f62\u3078\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h4>\u7b49\u6bd4\u6570\u5217\u578b\u3078\u5909\u5f62\u3057\u3001\u4e00\u822c\u9805\u3092\u5f97\u308b<\/h4>\n<p>\\(x=1,2\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(b_n=\\displaystyle\\frac{a_n-1}{a_n-2}\\)<\/li>\n<\/ul>\n<p>\u306a\u304a\\(n\\)\u3092\\(n+1\\)\u306b\u5909\u3048\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(b_{n+1}=\\displaystyle\\frac{a_{n+1}-1}{a_{n+1}-2}\\)<\/li>\n<\/ul>\n<p>\\(a_{n+1}=\\displaystyle\\frac{4a_n-2}{a_n+1}\\)\u3067\u3042\u308b\u305f\u3081\u3001\\(b_{n+1}=\\displaystyle\\frac{a_{n+1}-1}{a_{n+1}-2}\\)\u3078\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(b_{n+1}=\\displaystyle\\frac{a_{n+1}-1}{a_{n+1}-2}\\)<\/p>\n<p>\\(b_{n+1}=\\displaystyle\\frac{\\displaystyle\\frac{4a_n-2}{a_n+1}-1}{\\displaystyle\\frac{4a_n-2}{a_n+1}-2}\\)<\/p>\n<p>\\(b_{n+1}=\\displaystyle\\frac{3a_n-3}{2a_n-4}\\)<\/p>\n<p>\\(b_{n+1}=\\displaystyle\\frac{3(a_n-1)}{2(a_n-2)}\\)<\/p>\n<p>\\(b_{n+1}=\\displaystyle\\frac{3}{2}\u00b7\\displaystyle\\frac{a_n-1}{a_n-2}\\)<\/p>\n<p>\\(b_{n+1}=\\displaystyle\\frac{3}{2}b_n\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u6570\u5217\\(\\{b_n\\}\\)\u306f\u521d\u9805\\(b_1=\\displaystyle\\frac{a_1-1}{a_1-2}\\)\\(=2\\)\u3001\u516c\u6bd4\\(\\displaystyle\\frac{3}{2}\\)\u306e\u7b49\u6bd4\u6570\u5217\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u3001\u6570\u5217\\(\\{b_n\\}\\)\u306e\u4e00\u822c\u9805\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(b_n=2\u00b7\\left(\\displaystyle\\frac{3}{2}\\right)^{n-1}\\)<\/li>\n<\/ul>\n<p>\u307e\u305f\\(b_n=\\displaystyle\\frac{a_n-1}{a_n-2}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(b_n=\\displaystyle\\frac{a_n-1}{a_n-2}\\)<\/p>\n<p>\\(b_n(a_n-2)=a_n-1\\)<\/p>\n<p>\\(a_n\u00b7b_n-a_n=2b_n-1\\)<\/p>\n<p>\\(a_n(b_n-1)=2b_n-1\\)<\/p>\n<p>\\(a_n=\\displaystyle\\frac{2b_n-1}{b_n-1}\\)<\/p>\n<p>\u5148\u307b\u3069\u8a08\u7b97\u3057\u305f\u901a\u308a\u3001\\(b_n=2\u00b7\\left(\\displaystyle\\frac{3}{2}\\right)^{n-1}\\)\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u5f0f\u3092\u4ee3\u5165\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a_n=\\displaystyle\\frac{2b_n-1}{b_n-1}\\)<\/p>\n<p>\\(a_n=\\displaystyle\\frac{2\u00b72\u00b7\\left(\\displaystyle\\frac{3}{2}\\right)^{n-1}-1}{2\u00b7\\left(\\displaystyle\\frac{3}{2}\\right)^{n-1}-1}\\)<\/p>\n<p>\\(a_n=\\displaystyle\\frac{4\u00b73^{n-1}-2^{n-1}}{2\u00b73^{n-1}-2^{n-1}}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u7279\u6027\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u7740\u76ee\u3057\u3066\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u89e3\u304d\u65b9\u3092\u77e5\u3063\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u6f38\u5316\u5f0f\u3067\u7b54\u3048\u3092\u5f97\u308b\u306e\u306f\u96e3\u3057\u3044\u3067\u3059\u3002\u7279\u306b\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3067\u306f\u3001\u89e3\u304d\u65b9\u3092\u5b66\u3070\u305a\u306b\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3059\u308b\u306e\u306f\u4e0d\u53ef\u80fd\u306b\u8fd1\u3044\u3067\u3059\u3002<\/p>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u30012\u30d1\u30bf\u30fc\u30f3\u306b\u5206\u3051\u307e\u3057\u3087\u3046\u3002\u7279\u6027\u65b9\u7a0b\u5f0f\u304c\u91cd\u89e3\u3092\u3082\u3064\u5834\u5408\u3001\u6f38\u5316\u5f0f\u3092\u5909\u5f62\u5f8c\u3001\u9006\u6570\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u3063\u3066\u7b49\u5dee\u6570\u5217\u578b\u306e\u6f38\u5316\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u4e00\u822c\u9805\u3092\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3067\u7279\u6027\u65b9\u7a0b\u5f0f\u304c2\u3064\u306e\u7570\u306a\u308b\u89e3\u3092\u3082\u3064\u5834\u5408\u3001\\(b_n=\\displaystyle\\frac{a_n-\u03b1}{a_n-\u03b2}\\)\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u7279\u6b8a\u306a\u516c\u5f0f\u3067\u306f\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u308c\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3092\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u306f\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3067\u4e00\u822c\u9805\u3092\u5f97\u305f\u3044\u5834\u5408\u3001\u3053\u3053\u3067\u89e3\u8aac\u3057\u305f\u65b9\u6cd5\u306b\u3066\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u5b66\u306e\u4e2d\u3067\u3082\u3001\u5b8c\u5168\u306a\u308b\u6697\u8a18\u79d1\u76ee\u3068\u306a\u308b\u306e\u304c\u6f38\u5316\u5f0f\u3067\u3059\u3002\u89e3\u304d\u65b9\u3092\u899a\u3048\u3066\u3044\u308c\u3070\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3082\u306e\u306e\u3001\u89e3\u304d\u65b9\u3092\u899a\u3048\u3066\u3044\u306a\u3051\u308c\u3070\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3082\u540c\u69d8\u3067\u3059\u3002 \u5206\u6570\u5f62\u306e\u6f38\u5316\u5f0f\u3067\u306f\u9006\u6570\u3092\u5229\u7528\u3057 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":12149,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":{"0":"post-12133","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\/12133","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=12133"}],"version-history":[{"count":12,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12133\/revisions"}],"predecessor-version":[{"id":12199,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/posts\/12133\/revisions\/12199"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media\/12149"}],"wp:attachment":[{"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/media?parent=12133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/categories?post=12133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hatsudy.com\/jp\/wp-json\/wp\/v2\/tags?post=12133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}