{"id":248,"date":"2012-01-01T22:39:29","date_gmt":"2012-01-01T13:39:29","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=248"},"modified":"2021-03-16T17:03:12","modified_gmt":"2021-03-16T08:03:12","slug":"tkr200802","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr200802\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2008\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\u767d\u9ed2 \\(2\\) \u7a2e\u985e\u306e\u30ab\u30fc\u30c9\u304c\u305f\u304f\u3055\u3093\u3042\u308b. \u305d\u306e\u3046\u3061 \\(k\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u624b\u3082\u3068\u306b\u3082\u3063\u3066\u3044\u308b\u3068\u304d, \u6b21\u306e\u64cd\u4f5c (A) \u3092\u8003\u3048\u308b.<\/p>\r\n<ol>\r\n<li>(A)\u3000\u624b\u6301\u3061\u306e \\(k\\) \u679a\u306e\u4e2d\u304b\u3089 \\(1\\) \u679a\u3092, \u7b49\u78ba\u7387 \\(\\dfrac{1}{k}\\) \u3067\u9078\u3073\u51fa\u3057, \u305d\u308c\u3092\u9055\u3046\u8272\u306e\u30ab\u30fc\u30c9\u306b\u3068\u308a\u304b\u3048\u308b.<\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0b\u306e\u554f <strong>(1)<\/strong> , <strong>(2)<\/strong> \u306b\u7b54\u3048\u3088.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u6700\u521d\u306b\u767d \\(2\\) \u679a, \u9ed2 \\(2\\) \u679a, \u5408\u8a08 \\(4\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u3082\u3063\u3066\u3044\u308b\u3068\u304d,\r\n\u64cd\u4f5c (A) \u3092 \\(n\\) \u56de\u7e70\u308a\u8fd4\u3057\u305f\u5f8c\u306b\u521d\u3081\u3066, \\(4\\) \u679a\u3068\u3082\u540c\u3058\u8272\u306e\u30ab\u30fc\u30c9\u306b\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\u6700\u521d\u306b\u767d \\(3\\) \u679a, \u9ed2 \\(3\\) \u679a, \u5408\u8a08 \\(6\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u3082\u3063\u3066\u3044\u308b\u3068\u304d,\r\n\u64cd\u4f5c (A) \u3092 \\(n\\) \u56de\u7e70\u308a\u8fd4\u3057\u305f\u5f8c\u306b\u521d\u3081\u3066, \\(6\\) \u679a\u3068\u3082\u540c\u3058\u8272\u306e\u30ab\u30fc\u30c9\u306b\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/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>\u64cd\u4f5c (A) \u3092 \\(n\\) \u56de\u7e70\u308a\u8fd4\u3057\u305f\u5f8c, \\(2\\) \u8272\u306e\u30ab\u30fc\u30c9\u304c \\(2\\) \u679a\u305a\u3064\u3068\u306a\u308b\u78ba\u7387\u3092 \\(a _ n\\) ,\r\n\\(1\\) \u679a\u3068 \\(3\\) \u679a\u3067\u3042\u308b\u78ba\u7387\u3092 \\(b _ n\\) \u3068\u304a\u304f. \u305f\u3060\u3057, \\(1\\) \u5ea6\u3067\u3082 \\(4\\) \u679a\u306e\u30ab\u30fc\u30c9\u304c\u540c\u3058\u8272\u306b\u306a\u308b\u5834\u5408\u306f\u9664\u3044\u3066\u8003\u3048\u308b.<br \/>\r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\na _ {n+1} =\\dfrac{3}{4} b _ n & , \\quad b _ {n+1} =a _ n \\\\\r\n\\text{\u2234} \\quad b _ {n+2} & = \\dfrac{3}{4} b _ n\r\n\\end{align}\\]\r\n\\(b _ 0 =0\\) , \\(b _ 1 =1\\) \u306a\u306e\u3067<\/p>\r\n<ul>\r\n<li><p>\\(n\\) \u304c\u5076\u6570\u306e\u3068\u304d\u3000\\(b _ n =0\\)<\/p><\/li>\r\n<li><p>\\(n\\) \u304c\u5947\u6570\u306e\u3068\u304d\u3000\\(b _ n =\\left( \\dfrac{3}{4} \\right)^{\\frac{n-1}{2}}\\)<\/p><\/li>\r\n<\/ul>\r\n<p>\u6c42\u3081\u308b\u78ba\u7387\u306f, \\(\\dfrac{1}{4} b _ {n-1} \\quad ( n \\geqq 2 )\\) \u3068\u8868\u305b\u308b\u306e\u3067<\/p>\r\n<ul>\r\n<li><p>\\(n\\) \u304c\u5076\u6570\u306e\u3068\u304d\u3000\\(\\underline{\\dfrac{1}{4} \\left( \\dfrac{3}{4} \\right)^{\\frac{n}{2}-1}}\\)<\/p><\/li>\r\n<li><p>\\(n\\) \u304c\u5947\u6570\u306e\u3068\u304d\u3000\\(\\underline{0}\\)<\/p><\/li>\r\n<\/ul>\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u64cd\u4f5c (A) \u3092 \\(n\\) \u56de\u7e70\u308a\u8fd4\u3057\u305f\u5f8c, \\(2\\) \u8272\u306e\u30ab\u30fc\u30c9\u304c \\(3\\) \u679a\u305a\u3064\u3068\u306a\u308b\u78ba\u7387\u3092 \\(p _ n\\) ,\r\n\\(2\\) \u679a\u3068 \\(4\\) \u679a\u3067\u3042\u308b\u78ba\u7387\u3092 \\(q _ n\\) , \\(1\\) \u679a\u3068 \\(5\\) \u679a\u3067\u3042\u308b\u78ba\u7387\u3092 \\(r _ n\\) \u3068\u304a\u304f.\r\n\u305f\u3060\u3057, \\(1\\) \u5ea6\u3067\u3082 \\(6\\) \u679a\u306e\u30ab\u30fc\u30c9\u304c\u540c\u3058\u8272\u306b\u306a\u308b\u5834\u5408\u306f\u9664\u3044\u3066\u8003\u3048\u308b.<br \/>\r\n\u3053\u306e\u3068\u304d\r\n\\[\\begin{align}\r\np _ {n+1} & = \\dfrac{2}{3} q _ n , \\quad q _ {n+1} =p _ n +\\dfrac{5}{6} r _ n , \\quad r _ {n+1} =\\dfrac{1}{3} q _ n \\\\\r\n\\text{\u2234} \\quad q _ {n+2} & =p _ {n+1} +\\dfrac{5}{6} r _ {n+1} = \\dfrac{2}{3} q _ n +\\dfrac{5}{18} q _ n = \\dfrac{17}{18} q _ n\r\n\\end{align}\\]\r\n\\(q _ 0 =0\\) , \\(q _ 1 =1\\) \u306a\u306e\u3067,<\/p>\r\n<ul>\r\n<li><p>\\(n\\) \u304c\u5076\u6570\u306e\u3068\u304d\u3000\\(q _ n =0\\)<\/p><\/li>\r\n<li><p>\\(n\\) \u304c\u5947\u6570\u306e\u3068\u304d\u3000\\(q _ n =\\left( \\dfrac{17}{18} \\right)^{\\frac{n-1}{2}}\\)<\/p><\/li>\r\n<\/ul>\r\n<p>\u6c42\u3081\u308b\u78ba\u7387\u306f, \\(\\dfrac{1}{3} \\cdot \\dfrac{1}{6} q _ {n-2} =\\dfrac{1}{18} q _ {n-2}\\) \uff08 \\(n \\geqq 3\\) \uff09\u3068\u8868\u305b\u308b\u306e\u3067<\/p>\r\n<ul>\r\n<li><p>\\(n=1\\) , \\(n\\) \u304c\u5076\u6570\u306e\u3068\u304d\u3000\\(\\underline{0}\\)<\/p><\/li>\r\n<li><p>\\(n\\) \u304c \\(3\\) \u4ee5\u4e0a\u306e\u5947\u6570\u306e\u3068\u304d\u3000\\(\\underline{\\dfrac{1}{18} \\left( \\dfrac{17}{18} \\right)^{\\frac{n-3}{2}}}\\)<\/p><\/li>\r\n<\/ul>\r\n","protected":false},"excerpt":{"rendered":"\u767d\u9ed2 \\(2\\) \u7a2e\u985e\u306e\u30ab\u30fc\u30c9\u304c\u305f\u304f\u3055\u3093\u3042\u308b. \u305d\u306e\u3046\u3061 \\(k\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u624b\u3082\u3068\u306b\u3082\u3063\u3066\u3044\u308b\u3068\u304d, \u6b21\u306e\u64cd\u4f5c (A) \u3092\u8003\u3048\u308b. (A)\u3000\u624b\u6301\u3061\u306e \\(k\\) \u679a\u306e\u4e2d\u304b\u3089 \\(1\\) \u679a\u3092, \u7b49\u78ba\u7387 \\(\\dfr &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkr200802\/\">\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":[17],"tags":[139,16],"class_list":["post-248","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2008","tag-tokyo_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/248","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=248"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/248\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=248"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}