{"id":1224,"date":"2015-08-13T23:07:34","date_gmt":"2015-08-13T14:07:34","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1224"},"modified":"2021-03-09T16:01:27","modified_gmt":"2021-03-09T07:01:27","slug":"tkr201502","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr201502\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2015\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\u3069\u306e\u76ee\u3082\u51fa\u308b\u78ba\u7387\u304c \\(\\dfrac{1}{6}\\) \u306e\u3055\u3044\u3053\u308d\u3092 \\(1\\) \u3064\u7528\u610f\u3057, \u6b21\u306e\u3088\u3046\u306b\u5de6\u304b\u3089\u9806\u306b\u6587\u5b57\u3092\u66f8\u304f.<br \/>\r\n\u3055\u3044\u3053\u308d\u3092\u6295\u3052, \u51fa\u305f\u76ee\u304c \\(1, 2, 3\\) \u306e\u3068\u304d\u306f\u6587\u5b57\u5217 A A \u3092\u66f8\u304d, \\(4\\) \u306e\u3068\u304d\u306f\u6587\u5b57 B \u3092, \\(5\\) \u306e\u3068\u304d\u306f\u6587\u5b57 C \u3092, \\(6\\) \u306e\u3068\u304d\u306f\u6587\u5b57 D \u3092\u66f8\u304f. \u3055\u3089\u306b\u7e70\u308a\u8fd4\u3057\u3055\u3044\u3053\u308d\u3092\u6295\u3052, \u540c\u3058\u898f\u5247\u306b\u5f93\u3063\u3066, A A, B, C, D \u3092\u3059\u3067\u306b\u3042\u308b\u6587\u5b57\u5217\u306e\u53f3\u5074\u306b\u3064\u306a\u3052\u3066\u66f8\u3044\u3066\u3044\u304f.<br \/>\r\n\u305f\u3068\u3048\u3070, \u3055\u3044\u3053\u308d\u3092 \\(5\\) \u56de\u6295\u3052, \u305d\u306e\u51fa\u305f\u76ee\u304c\u9806\u306b \\(2, 5, 6, 3, 4\\) \u3067\u3042\u3063\u305f\u3068\u3059\u308b\u3068, \u5f97\u3089\u308c\u308b\u6587\u5b57\u5217\u306f\r\n\\[\r\n\\text{A A C D A A B}\r\n\\]\r\n\u3068\u306a\u308b. \u3053\u306e\u3068\u304d, \u5de6\u304b\u3089 \\(4\\) \u756a\u76ee\u306e\u6587\u5b57\u306f D, \\(5\\) \u756a\u76ee\u306e\u6587\u5b57\u306f A \u3067\u3042\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(n\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. \\(n\\) \u56de\u3055\u3044\u3053\u308d\u3092\u6295\u3052, \u6587\u5b57\u5217\u3092\u3064\u304f\u308b\u3068\u304d, \u6587\u5b57\u5217\u306e\u5de6\u304b\u3089 \\(n\\) \u756a\u76ee\u306e\u6587\u5b57\u304c A \u3068\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b. \\(n\\) \u56de\u3055\u3044\u3053\u308d\u3092\u6295\u3052, \u6587\u5b57\u5217\u3092\u4f5c\u308b\u3068\u304d, \u6587\u5b57\u5217\u306e\u5de6\u304b\u3089 \\(n-1\\) \u756a\u76ee\u306e\u6587\u5b57\u304c A \u3067, \u304b\u3064 \\(n\\) \u756a\u76ee\u306e\u6587\u5b57\u304c B \u3068\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>\u6c42\u3081\u308b\u78ba\u7387\u3092 \\(p _ n\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\np _ 1 & = \\dfrac{1}{2} , \\\\\r\np _ 2 & = \\dfrac{1}{2} +\\dfrac{1}{2} \\cdot \\dfrac{1}{2} = \\dfrac{3}{4}\r\n\\end{align}\\]\r\n\\(n \\geqq 3\\) \u306e\u3068\u304d, \u6761\u4ef6\u3092\u307f\u305f\u3059\u4e8b\u8c61\uff08\u5de6\u304b\u3089 \\(n\\) \u756a\u76ee\u304c A \uff09\u306f, \u4ee5\u4e0b\u306e \\(2\\) \u3064\u5834\u5408\u304c\u8003\u3048\u3089\u308c\u308b.<\/p>\r\n<ul>\r\n<li><p>\\(1\\) \u56de\u76ee\u306b, \\(1, 2, 3\\) \u304c\u51fa\u305f\u5834\u5408, \u6b21\u306e \\(n-2\\) \u56de\u3067, \u6761\u4ef6\u3092\u307f\u305f\u3059\u4e8b\u8c61\uff08\u521d\u3081\u306e A A \u3092\u9664\u3044\u3066, \u5de6\u304b\u3089 \\(n-2\\) \u756a\u76ee\u304c A \uff09\u304c\u8d77\u3053\u308b.<\/p><\/li>\r\n<li><p>\\(1\\) \u56de\u76ee\u306b, \\(4, 5, 6\\) \u304c\u51fa\u305f\u5834\u5408, \u6b8b\u308a \\(n-1\\) \u56de\u3067, \u6761\u4ef6\u3092\u307f\u305f\u3059\u4e8b\u8c61\uff08\u521d\u3081\u306e \\(1\\) \u6587\u5b57\u3092\u9664\u3044\u3066, \u5de6\u304b\u3089 \\(n-1\\) \u756a\u76ee\u304c A \uff09\u304c\u8d77\u3053\u308b.<\/p><\/li>\r\n<\/ul>\r\n<p>\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\np _ n = \\dfrac{1}{2} p _ {n-1} +\\dfrac{1}{2} p _ {n-2}\r\n\\]\r\n\u3053\u308c\u3092\u5909\u5f62\u3059\u308b\u3068\r\n\\[\r\np _ n -p _ {n-1} = -\\dfrac{1}{2} \\left( p _ {n-1} -p _ {n-2} \\right)\r\n\\]\r\n\u3086\u3048\u306b, \u6570\u5217 \\(\\{ p _ n -p _ {n-1} \\}\\) \u306f, \u521d\u9805 \\(p _ 2 -p _ 1 = \\dfrac{1}{4}\\) , \u516c\u6bd4 \\(-\\dfrac{1}{2}\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\r\np _ n -p _ {n-1} = \\dfrac{1}{4} \\left( -\\dfrac{1}{2} \\right)^{n-2} = \\left( -\\dfrac{1}{2} \\right)^n\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\np _ n & = p _ 1 +\\textstyle\\sum\\limits _ {k=2}^n \\left( -\\dfrac{1}{2} \\right)^k \\\\\r\n& = \\dfrac{1}{2} +\\dfrac{1}{4} \\cdot \\dfrac{1 -\\left( -\\frac{1}{2} \\right)^{n-1}}{1 +\\frac{1}{2}} \\\\\r\n& = \\dfrac{1}{2} +\\dfrac{1}{6} \\left\\{ 1 -\\left( -\\dfrac{1}{2} \\right)^{n-1} \\right\\} \\\\\r\n& = \\underline{\\dfrac{2}{3} +\\dfrac{1}{3} \\left( -\\dfrac{1}{2} \\right)^n}\r\n\\end{align}\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u6c42\u3081\u308b\u78ba\u7387\u3092 \\(q _ n \\ ( n \\geqq 2 )\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\nq _ 2 & = 0 \\\\\r\nq _ 3 & = \\dfrac{1}{2} \\cdot \\dfrac{1}{6} = \\dfrac{1}{12}\r\n\\end{align}\\]\r\n<p><strong>(1)<\/strong> \u3068\u540c\u69d8\u306b\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\r\n\\[\r\nq _ n = \\dfrac{1}{2} q _ {n-1} +\\dfrac{1}{2} q _ {n-2}\r\n\\]\r\n\u4ee5\u964d\u3082, <strong>(1)<\/strong> \u3068\u540c\u69d8\u306b\u8003\u3048\u308b.<br \/>\r\n\u6570\u5217 \\(\\{ q _ n -q _ {n-1} \\}\\) \u306f, \u521d\u9805 \\(q _ 3 -q _ 2 = \\dfrac{1}{12}\\) , \u516c\u6bd4 \\(-\\dfrac{1}{2}\\) \u306e\u7b49\u6bd4\u6570\u5217\u306a\u306e\u3067\r\n\\[\r\nq _ n -q _ {n-1} = \\dfrac{1}{12} \\left( -\\dfrac{1}{2} \\right)^{n-3} = \\dfrac{1}{3} \\left( -\\dfrac{1}{2} \\right)^{n-1}\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\nq _ n & = q _ 2 +\\textstyle\\sum\\limits _ {k=3}^n \\dfrac{1}{3} \\left( -\\dfrac{1}{2} \\right)^{k-1} \\\\\r\n& = 0 +\\dfrac{1}{12} \\cdot \\dfrac{1 -\\left( -\\frac{1}{2} \\right)^{n-2}}{1 +\\frac{1}{2}} \\\\\r\n& = \\underline{\\dfrac{1}{18} \\left\\{ 1 -\\left( -\\dfrac{1}{2} \\right)^{n-2} \\right\\}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u3069\u306e\u76ee\u3082\u51fa\u308b\u78ba\u7387\u304c \\(\\dfrac{1}{6}\\) \u306e\u3055\u3044\u3053\u308d\u3092 \\(1\\) \u3064\u7528\u610f\u3057, \u6b21\u306e\u3088\u3046\u306b\u5de6\u304b\u3089\u9806\u306b\u6587\u5b57\u3092\u66f8\u304f. \u3055\u3044\u3053\u308d\u3092\u6295\u3052, \u51fa\u305f\u76ee\u304c \\(1, 2, 3\\) \u306e\u3068\u304d\u306f\u6587\u5b57\u5217 A A \u3092\u66f8\u304d, \\(4\\ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkr201502\/\">\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":[125],"tags":[139,137],"class_list":["post-1224","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2015","tag-tokyo_r","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1224","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=1224"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1224\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}