{"id":335,"date":"2012-03-07T01:00:34","date_gmt":"2012-03-06T16:00:34","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=335"},"modified":"2021-10-03T20:50:17","modified_gmt":"2021-10-03T11:50:17","slug":"kbr200804","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kbr200804\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2008\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u4e8c\u3064\u306e\u6570\u5217 \\(\\{ a _ n \\} , \\{ b _ n \\}\\) \u3092\u6b21\u306e\u6f38\u5316\u5f0f\u306b\u3088\u3063\u3066\u5b9a\u3081\u308b.\r\n\\[\\begin{align}\r\na _ 1 & =3 , \\ b _ 1 =1 \\\\\r\na _ {n+1} & = \\dfrac{1}{2} \\left( 3a _ n +5b _ n \\right) \\\\\r\nb _ {n+1} & = \\dfrac{1}{2} \\left( a _ n +3b _ n \\right)\r\n\\end{align}\\]\r\n

    \r\n

  1. (1)<\/strong>\u3000\u3059\u3079\u3066\u306e\u81ea\u7136\u6570 \\(n\\) \u306b\u3064\u3044\u3066, \\({a _ n}^2 -5{b _ n}^2 = 4\\) \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u3059\u3079\u3066\u306e\u81ea\u7136\u6570 \\(n\\) \u306b\u3064\u3044\u3066, \\(a _ n , b _ n\\) \u306f\u81ea\u7136\u6570\u304b\u3064 \\(a _ n+b _ n\\) \u306f\u5076\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u3092\u7528\u3044\u3066\u793a\u3059.<\/p>\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(n = 1\\) \u306e\u3068\u304d\r\n\\[\r\n{a _ 1}^2 -5{b _ 1}^2 =9-5 = 4\r\n\\]\r\n\u306a\u306e\u3067, \\(n=1\\) \u306e\u3068\u304d\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n

    2. 2*<\/strong>\u3000\\(n = k\\) \u306e\u3068\u304d, \u6210\u7acb\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n{a _ {k+1}}^2 & -5{b _ {k+1}}^2 \\\\\r\n& =\\dfrac{1}{4} \\left( 9{a _ k}^2 +30 a _ k b _ k +25{b _ k}^2 -5{a _ k}^2 -30 a _ k b _ k -45{b _ k}^2\\right) \\\\\r\n& ={a _ k}^2 -5{b _ k}^2 = 4\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(n=k+1\\) \u306e\u3068\u304d\u3082\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n

      (2)<\/strong><\/p>\r\n

      \u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u3092\u7528\u3044\u3066\u793a\u3059.<\/p>\r\n

        \r\n

      1. 1*<\/strong>\u3000\\(n = 1\\) \u306e\u3068\u304d, \u6761\u4ef6\u3088\u308a\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n

      2. 2*<\/strong>\u3000\\(n = k\\) \u306e\u3068\u304d, \u6210\u7acb\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068
        \r\n\\(a _ k\\) \u3068 \\(b _ k\\) \u306e\u5947\u9047\u306f\u4e00\u81f4\u3057\u3066\u3044\u308b.
        \r\n\\(3a _ k\\) \u3068 \\(5b _ k\\) , \\(a _ k\\) \u3068 \\(3b _ k\\) \u306e\u5947\u9047\u306f\u4e00\u81f4\u3059\u308b\u306e\u3067, \\(3a _ k +5b _ k\\) , \\(a _ k +3b _ k\\) \u306f\u3068\u3082\u306b\u5076\u6570\u3067\u3042\u308b.
        \r\n\u3057\u305f\u304c\u3063\u3066, \\(a _ {k+1} , b _ {k+1}\\) \u306f\u3068\u3082\u306b\u81ea\u7136\u6570\u3067\u3042\u308b.
        \r\n\u307e\u305f\r\n\\[\r\na _ {k+1} +b _ {k+1} = 2 \\left( a _ k +2b _ k \\right)\r\n\\]\r\n\u306a\u306e\u3067, \\(a _ {k+1} +b _ {k+1}\\) \u306f\u5076\u6570\u3067\u3042\u308b.
        \r\n\u3086\u3048\u306b, \\(n=k+1\\) \u306e\u3068\u304d\u3082\u6210\u7acb\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n

        \u4ee5\u4e0a\u3088\u308a, \u984c\u610f\u306f\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\u4e8c\u3064\u306e\u6570\u5217 \\(\\{ a _ n \\} , \\{ b _ n \\}\\) \u3092\u6b21\u306e\u6f38\u5316\u5f0f\u306b\u3088\u3063\u3066\u5b9a\u3081\u308b. \\[\\begin{align} a _ 1 & =3 , \\ b _ 1 =1 \\\\ a _ {n+1} & = \\d … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[55],"tags":[144,16],"class_list":["post-335","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2008","tag-tsukuba_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/335","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=335"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/335\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=335"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=335"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}