{"id":12154,"date":"2023-01-09T13:44:29","date_gmt":"2023-01-09T04:44:29","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=12154"},"modified":"2023-01-11T18:52:16","modified_gmt":"2023-01-11T09:52:16","slug":"recurrence-relation-5","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/recurrence-relation-5.html","title":{"rendered":"\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\uff1a\u516c\u5f0f\u3068\u4e00\u822c\u9805\u306e\u8a08\u7b97\u65b9\u6cd5"},"content":{"rendered":"\n<p>\u7279\u6b8a\u306a\u6f38\u5316\u5f0f\u306f\u591a\u304f\u3001\u305d\u306e\u4e2d\u306b\u548c\\(S_n\\)\u3092\u542b\u3080\u6f38\u5316\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002\u6570\u5217\u3067\u306e\u548c\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u6f38\u5316\u5f0f\u306f\u89e3\u304d\u65b9\u304c\u6c7a\u307e\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u89e3\u304d\u65b9\u3092\u899a\u3048\u3066\u3044\u306a\u3051\u308c\u3070\u7b54\u3048\u3092\u5f97\u308b\u306e\u306f\u96e3\u3057\u3044\u3067\u3059\u3002\u30d2\u30f3\u30c8\u306a\u3057\u306b\u6f38\u5316\u5f0f\u306e\u7b54\u3048\u3092\u5f97\u308b\u306e\u306f\u96e3\u6613\u5ea6\u304c\u9ad8\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u306b\u3064\u3044\u3066\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u899a\u3048\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u306b\u95a2\u3059\u308b\u554f\u984c\u3067\u306f\u5177\u4f53\u7684\u306b\u3069\u306e\u3088\u3046\u306b\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u548c\\(S_n\\)\u3068\u4e00\u822c\u9805\\(a_n\\)\u306e\u95a2\u4fc2\u3068\u516c\u5f0f<\/h2>\n<p>\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u3001\u548c\\(S_n\\)\u3068\u4e00\u822c\u9805\\(a_n\\)\u306e\u95a2\u4fc2\u3092\u5fa9\u7fd2\u3057\u307e\u3057\u3087\u3046\u3002\u6570\u5217\u306e\u548c\\(S_n\\)\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u4e00\u822c\u9805\\(a_n\\)\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3001\\(S_n\\)\u3068\\(S_{n-1}\\)\u3092\u5229\u7528\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(S_n-S_{n-1}=a_n\\)<\/li>\n<li>\\(n\u22672\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/12\/djeh8.jpg\" alt=\"\" width=\"600\" height=\"143\" class=\"aligncenter size-full wp-image-12007\" \/><\/p>\n<p>\u305f\u3060\u6f38\u5316\u5f0f\u3067\u306f\u3001\\(n\\)\u3092\\(n+1\\)\u306b\u5909\u3048\u308b\u3068\u304d\u306e\u5f0f\u304c\u3072\u3093\u3071\u3093\u306b\u5229\u7528\u3055\u308c\u307e\u3059\u3002\u305d\u3053\u3067\\(S_n\\)\u3068\\(S_{n-1}\\)\u3067\u306f\u306a\u304f\u3001\\(S_n\\)\u3068\\(S_{n+1}\\)\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u5834\u5408\u3001\\(a_{n+1}\\)\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(S_{n+1}-S_n=a_{n+1}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2023\/01\/rjeh2.jpg\" alt=\"\" width=\"600\" height=\"143\" class=\"aligncenter size-full wp-image-12203\" \/><\/p>\n<p>\u516c\u5f0f\u3068\u3057\u3066\u899a\u3048\u306a\u304f\u3066\u3082\u3001\u5bb9\u6613\u306b\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u3053\u3053\u307e\u3067\u306e\u5185\u5bb9\u3092\u7406\u89e3\u3057\u3066\u3001\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u306e\u554f\u984c\u3092\u89e3\u3051\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u548c\\(S_n\\)\u3092\u542b\u3080\u6f38\u5316\u5f0f\u3067\u521d\u9805\u3092\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u305d\u308c\u3067\u306f\u3001\u4f8b\u984c\u3092\u7528\u3044\u3066\u548c\\(S_n\\)\u3092\u542b\u3080\u6f38\u5316\u5f0f\u306e\u4e00\u822c\u9805\\(a_n\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u6570\u5217\\(\\{a_n\\}\\)\u306b\u3064\u3044\u3066\u3001\u521d\u9805\u304b\u3089\u7b2c\\(n\\)\u9805\u307e\u3067\u306e\u548c\u304c\\(S_n=7a_n-3-3n\\)\u306e\u3068\u304d\u3001\u4e00\u822c\u9805\\(a_n\\)\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\u548c\\(S_n\\)\u3092\u542b\u3080\u6f38\u5316\u5f0f\u3067\u306f\u3001\\(a_n\\)\u306e\u307f\u3092\u542b\u3080\u5f0f\u306b\u5909\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u307e\u305a\u306f\u521d\u9805\\(a_1\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\\(S_1=a_1\\)\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308c\u307e\u3059\u3002<\/p>\n<p>\\(S_1=7a_1-3-3\u00d71\\)<\/p>\n<p>\\(a_1=7a_1-6\\)<\/p>\n<p>\\(-6a_1=-6\\)<\/p>\n<p>\\(a_1=1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u521d\u9805\u306f\\(a_1=1\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h3>\u9805\u6570\u3092\u305a\u3089\u3057\u3001\u6f38\u5316\u5f0f\u3092\u5909\u5f62\u3059\u308b<\/h3>\n<p>\u6b21\u306b\u3001\\(S_n\\)\u3068\\(S_{n+1}\\)\u3092\u5229\u7528\u3057\u3066\u5f0f\u3092\u4f5c\u308a\u307e\u3059\u3002\u554f\u984c\u6587\u3088\u308a\u3001\\(S_{n+1}\\)\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(S_{n+1}=7a_{n+1}-3-3(n+1)\\)<\/p>\n<p>\\(S_{n+1}=7a_{n+1}-6-3n\\)<\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(S_{n+1}-S_n=a_{n+1}\\)<\/p>\n<p>\\(7a_{n+1}-6-3n\\)\\(-(7a_n-3-3n)\\)\\(=a_{n+1}\\)<\/p>\n<p>\\(6a_{n+1}=7a_n+3\\)<\/p>\n<p>\\(a_{n+1}=\\displaystyle\\frac{7}{6}a_n+\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u548c\\(S_n\\)\u3092\u542b\u3080\u6f38\u5316\u5f0f\u306b\u3064\u3044\u3066\u3001\\(S_n\\)\u3092\u542b\u307e\u306a\u3044\u6f38\u5316\u5f0f\u3078\u5909\u5f62\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h3>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u3001\u4e00\u822c\u9805\u3092\u5f97\u308b<\/h3>\n<p>\\(a_n\\)\u3092\u542b\u3080\u6f38\u5316\u5f0f\u3092\u4f5c\u308c\u3070\u3001\u6f38\u5316\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u3067\u3059\u3002\u5148\u307b\u3069\u306e\u5f0f\u306b\u3064\u3044\u3066\u3001\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\u03b1=\\displaystyle\\frac{7}{6}\u03b1+\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\\(-\\displaystyle\\frac{1}{6}\u03b1=\\displaystyle\\frac{1}{2}\\)<\/p>\n<p>\\(\u03b1=-3\\)<\/p>\n<p>\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3068\\(\u03b1=-3\\)\u306b\u306a\u308b\u305f\u3081\u3001\u5148\u307b\u3069\u306e\u6f38\u5316\u5f0f\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a_{n+1}+3=\\displaystyle\\frac{7}{6}(a_n+3)\\)<\/li>\n<\/ul>\n<p>\u6570\u5217\\(\\{a_n+3\\}\\)\u306f\u521d\u9805\\(a_1+3=4\\)\u3001\u516c\u6bd4\\(\\displaystyle\\frac{7}{6}\\)\u306e\u7b49\u6bd4\u6570\u5217\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e00\u822c\u9805\\(a_n\\)\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(a_n+3=4\u00b7\\left(\\displaystyle\\frac{7}{6}\\right)^{n-1}\\)<\/p>\n<p>\\(a_n=4\u00b7\\left(\\displaystyle\\frac{7}{6}\\right)^{n-1}-3\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u4e00\u822c\u9805\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u3067\u306f\u3001\\(S_n\\)\u3092\u6d88\u53bb\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3057\u3087\u3046\u3002\u305d\u3046\u3059\u308c\u3070\u3001\u4e00\u822c\u9805\u3092\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<h2>\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u5b66\u3076<\/h2>\n<p>\u6570\u5217\u306e\u548c\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u4e00\u822c\u9805\\(a_n\\)\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u6f38\u5316\u5f0f\u3067\u306f\u3001\\(S_n\\)\u3068\\(S_{n+1}\\)\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\\(a_{n+1}\\)\u3092\u4f5c\u308c\u307e\u3059\u3002\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6f38\u5316\u5f0f\u306e\u8a08\u7b97\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<p>\\(S_{n+1}-S_n=a_{n+1}\\)\u3067\u3042\u308a\u3001\\(S_1=a_1\\)\u3067\u3059\u3002\u3053\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u6f38\u5316\u5f0f\u3092\u5909\u5f62\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u6f38\u5316\u5f0f\u3067\\(S_n\\)\u3092\u6d88\u53bb\u3067\u304d\u308c\u3070\u3001\u3042\u3068\u306f\u6f38\u5316\u5f0f\u306e\u8a08\u7b97\u3092\u3059\u308b\u3060\u3051\u3067\u3059\u3002\u7279\u6027\u65b9\u7a0b\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4e00\u822c\u9805\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7279\u6b8a\u306a\u6f38\u5316\u5f0f\u306f\u591a\u304f\u3001\u305d\u306e\u4e2d\u306b\u548c\\(S_n\\)\u3092\u542b\u3080\u6f38\u5316\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002\u6570\u5217\u3067\u306e\u548c\u306e\u6027\u8cea\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u548c\u3092\u542b\u3080\u6f38\u5316\u5f0f\u3092\u89e3\u304f\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002 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