{"id":240,"date":"2011-12-03T00:40:05","date_gmt":"2011-12-02T15:40:05","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=240"},"modified":"2021-10-20T16:32:43","modified_gmt":"2021-10-20T07:32:43","slug":"ykr200903","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr200903\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2009\uff1a\u7b2c3\u554f"},"content":{"rendered":"<hr \/>\n<p>\u8d64, \u9752, \u9ec4\u306e \\(3\\) \u8272\u3092\u7528\u3044\u3066, \u6a2a\u4e00\u5217\u306b\u4e26\u3093\u3060 \\(n\\) \u500b\u306e\u30de\u30b9\u3092, \u96a3\u308a\u5408\u3046\u30de\u30b9\u306f\u7570\u306a\u308b\u8272\u306b\u306a\u308b\u3088\u3046\u306b\u5857\u308a\u5206\u3051\u308b.\r\n\u305f\u3060\u3057, \u4f7f\u308f\u306a\u3044\u8272\u304c\u3042\u3063\u3066\u3082\u3088\u3044. \u4e21\u7aef\u306e\u30de\u30b9\u304c\u540c\u3058\u8272\u306b\u306a\u308b\u5834\u5408\u306e\u6570\u3092 \\(a _ n\\) \u3068\u3057, \u4e21\u7aef\u306e\u30de\u30b9\u304c\u7570\u306a\u308b\u8272\u306b\u306a\u308b\u5834\u5408\u306e\u6570\u3092 \\(b _ n\\) \u3068\u3059\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(a _ 3 , b _ 3 , a _ 4 , b _ 4\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(a _ n , b _ n \\ ( n \\geqq 3 )\\) \u3092 \\(n\\) \u306e\u5f0f\u3067\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n<hr \/>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\u4e00\u822c\u306e\u81ea\u7136\u6570 \\(n\\) \u306b\u3064\u3044\u3066\u8003\u3048\u308b.\r\n\\[\r\na _ 1 =3 , \\ b _ 1 =0 , \\ a _ 2 = 0 , \\ b _ 2 = 6 \\quad ... [1]\r\n\\]\r\n\\(n\\) \u500b\u306e\u30de\u30b9\u304c\u4e26\u3076\u5217\u306b, \u305d\u306e\u53f3\u7aef\u306b \\(1\\) \u3064\u306e\u30de\u30b9\u3092\u52a0\u3048\u3066 \\(n+1\\) \u500b\u306e\u30de\u30b9\u306e\u5217\u3092\u4f5c\u308b\u3053\u3068\u3092\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\u4e21\u7aef\u304c\u540c\u3058\u8272\u306b\u306a\u308b\u5834\u5408<br \/>\r\n\u4e21\u7aef\u304c\u7570\u306a\u308b\u8272\u306e\u5217\u306b, \u5de6\u7aef\u3068\u540c\u3058\u8272\u306e\u30de\u30b9\u3092\u52a0\u3048\u308c\u3070\u3088\u3044\u306e\u3067\r\n\\[\r\na _ {n+1} = b _ n \\quad ... [2]\r\n\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\u4e21\u7aef\u304c\u7570\u306a\u308b\u8272\u306b\u306a\u308b\u5834\u5408<br \/>\r\n\u4ee5\u4e0b\u306e\u3044\u305a\u308c\u304b\u306e\u65b9\u6cd5\u3092\u3068\u308c\u3070\u3088\u3044.\r\n<ul>\r\n<li><p>\u4e21\u7aef\u304c\u7570\u306a\u308b\u8272\u306e\u5217\u306b, \u5de6\u7aef, \u53f3\u7aef\u306e\u3069\u3061\u3089\u3067\u3082\u306a\u3044\u8272\u306e\u30de\u30b9\u3092\u52a0\u3048\u308b.<\/p><\/li>\r\n<li><p>\u4e21\u7aef\u304c\u540c\u3058\u8272\u306e\u5217\u306b, \u7570\u306a\u308b \\(2\\) \u8272\u306e\u3044\u305a\u308c\u304b\u306e\u8272\u306e\u30de\u30b9\u3092\u52a0\u3048\u308b.<\/p><\/li>\r\n<\/ul>\r\n\u3086\u3048\u306b\r\n\\[\r\nb _ {n+1} = 2a _ n +b _ n \\quad .... [3]\r\n\\]<\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, [2] [3] \u3088\u308a\r\n\\[\\begin{align}\r\n& a _ {n+2} -a _ {n+1} -2a _ n = 0\\\\\r\n\\text{\u2234} \\quad & \\left\\{ \\begin{array}{l} a _ {n+2} -2a _ {n+1} = -\\left( a _ {n+1} -2a _ n \\right) \\\\ a _ {n+2} +a _ {n+1} = 2 \\left( a _ {n+1} +a _ n \\right) \\end{array} \\right.\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, [1] \u3082\u7528\u3044\u308c\u3070<\/p>\r\n<ul>\r\n<li><p>\\(\\{ a _ {n+1} -2a _ n \\}\\) \u306f\u521d\u9805 \\(a _ 2 -2a _ 1 = -6\\) , \u516c\u6bd4 \\(-1\\) \u306e\u7b49\u6bd4\u6570\u5217<\/p><\/li>\r\n<li><p>\\(\\{ a _ {n+1} +a _ n \\}\\) \u306f\u521d\u9805 \\(a _ 2 +a _ 1 = 3\\) , \u516c\u6bd4 \\(2\\) \u306e\u7b49\u6bd4\u6570\u5217<\/p><\/li>\r\n<\/ul>\r\n<p>\u306a\u306e\u3067\r\n\\[\\begin{align}\r\na _ {n+1} -2a _ n & = -6 (-1)^{n-1} = 6 \\left( -1 \\right)^n \\quad ... [4] \\\\\r\na _ {n+1} +a _ n & = 3 \\cdot 2^{n-1} \\quad ... [5]\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \\(\\dfrac{[5] -[4]}{3}\\) \u3088\u308a\r\n\\[\r\na _ n = \\dfrac{3 \\cdot 2^{n-1} -6 (-1)^n}{3} = 2^{n-1} +2 (-1)^{n-1}\r\n\\]\r\n\u307e\u305f\r\n\\[\r\nb _ n = a _ {n+1} = 2^n +2 (-1)^n\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\na _ 3 = 2^2 +2 = \\underline{6} & , \\ b _ 3 = 2^3 -2 = \\underline{6} \\\\\r\na _ 4 = b _ 3 = \\underline{6} & , \\ b _ 4 = 2^4 +2 = \\underline{18}\r\n\\end{align}\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\\[\r\na _ n = \\underline{2^{n-1} +2 (-1)^{n-1}} , \\ b _ n = \\underline{2^n +2 (-1)^n}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u8d64, \u9752, \u9ec4\u306e \\(3\\) \u8272\u3092\u7528\u3044\u3066, \u6a2a\u4e00\u5217\u306b\u4e26\u3093\u3060 \\(n\\) \u500b\u306e\u30de\u30b9\u3092, \u96a3\u308a\u5408\u3046\u30de\u30b9\u306f\u7570\u306a\u308b\u8272\u306b\u306a\u308b\u3088\u3046\u306b\u5857\u308a\u5206\u3051\u308b. \u305f\u3060\u3057, \u4f7f\u308f\u306a\u3044\u8272\u304c\u3042\u3063\u3066\u3082\u3088\u3044. \u4e21\u7aef\u306e\u30de\u30b9\u304c\u540c\u3058\u8272\u306b\u306a\u308b\u5834\u5408\u306e\u6570\u3092 \\(a _  &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/ykr200903\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[42],"tags":[15,9],"class_list":["post-240","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2009","tag-15","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/240","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=240"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/240\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}