{"id":1217,"date":"2015-07-31T23:47:10","date_gmt":"2015-07-31T14:47:10","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1217"},"modified":"2015-08-01T00:05:28","modified_gmt":"2015-07-31T15:05:28","slug":"htb201405","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201405\/","title":{"rendered":"\u4e00\u6a4b\u59272014\uff1a\u7b2c5\u554f"},"content":{"rendered":"\u6570\u76f4\u7dda\u4e0a\u306e\u70b9P\u3092\u6b21\u306e\u898f\u5247\u3067\u79fb\u52d5\u3055\u305b\u308b. \u4e00\u679a\u306e\u786c\u8ca8\u3092\u6295\u3052\u3066, \u8868\u304c\u51fa\u308c\u3070P\u3092 \\(+1\\) \u3060\u3051\u79fb\u52d5\u3055\u305b, \u88cf\u304c\u51fa\u308c\u3070P\u3092\u539f\u70b9\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u306b\u79fb\u52d5\u3055\u305b\u308b. P\u306f\u521d\u3081\u539f\u70b9\u306b\u3042\u308b\u3068\u3057, \u786c\u8ca8\u3092 \\(n\\) \u56de\u6295\u3052\u305f\u5f8c\u306eP\u306e\u5ea7\u6a19\u3092 \\(a_n\\) \u3068\u3059\u308b. \r\n<ol>\r\n<li><strong>(1)<\/strong>\u3000\\(a_3 = 0\\) \u3068\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088. <\/li>\r\n<li><strong>(2)<\/strong>\u3000\\(a_4 = 1\\) \u3068\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088. <\/li>\r\n<li><strong>(3)<\/strong>\u3000\\(n \\geqq 3\\) \u306e\u3068\u304d, \\(a_n = n-3\\) \u3068\u306a\u308b\u78ba\u7387\u3092 \\(n\\) \u3092\u7528\u3044\u3066\u8868\u305b. <\/li>\r\n<\/ol>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n\r\n\u8868, \u88cf\u304c\u51fa\u308b\u3053\u3068\u3092\u305d\u308c\u305e\u308cH, B\u3068\u8868\u3059\u3053\u3068\u3068\u3059\u308b. \r\n\r\n<strong>(1)<\/strong>\r\n\r\n\\(a_3 = 0\\) \u3068\u306a\u308b\u306e\u306f, \u300cBBB\u300d\u300cHBH\u300d\u3068\u306a\u308b\u3068\u304d\u306e\u307f\u306a\u306e\u3067, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{2}{2^3} = \\underline{\\dfrac{1}{4}}\r\n\\]\r\n\r\n<strong>(2)<\/strong>\r\n\r\n\\(a_4 = 1\\) \u3068\u306a\u308b\u306e\u306f\r\n<ul>\r\n<li>\\(a_3 = 0\\) \u304b\u3089, H\u3068\u306a\u308b\u5834\u5408<\/li>\r\n<li>\\(a_3 = -1\\) \u304b\u3089, B\u3068\u306a\u308b\u5834\u5408<\/li>\r\n<\/ul>\r\n\\(a_3 = 0\\) \u3068\u306a\u308b\u78ba\u7387\u306f, <strong>(1)<\/strong>\u306e\u7d50\u679c\u3088\u308a, \\(\\dfrac{1}{4}\\) .   \r\n\\(a_3 = -1\\) \u3068\u306a\u308b\u306e\u306f, \u300cBHB\u300d\u3068\u306a\u308b\u3068\u304d\u306e\u307f\u306a\u306e\u3067, \u305d\u306e\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{1}{2^3} = \\dfrac{1}{8}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\dfrac{1}{4} \\cdot \\dfrac{1}{2} +\\dfrac{1}{8} \\cdot \\dfrac{1}{2} = \\underline{\\dfrac{3}{16}}\r\n\\]\r\n\r\n<strong>(3)<\/strong>\r\n\r\n\u6c42\u3081\u308b\u78ba\u7387\u3092 \\(p_n\\) \u3068\u304a\u304f.   \r\n\\(n \\geqq 4\\) \u306e\u5834\u5408\u306b\u3064\u3044\u3066, <strong>(2)<\/strong>\u3068\u540c\u69d8\u306b\u8003\u3048\u308b.   \r\n\\(a_n = n-3\\) \u3068\u306a\u308b\u306e\u306f\r\n<ul>\r\n<li>\\(a_{n-1} = n-4\\) \u304b\u3089, H\u3068\u306a\u308b\u5834\u5408<\/li>\r\n<li>\\(a_{n-1} = -(n-3)\\) \u304b\u3089, B\u3068\u306a\u308b\u5834\u5408<\/li>\r\n<\/ul>\r\n\\(a_{n-1} = n-4\\) \u3068\u306a\u308b\u78ba\u7387\u306f, \\(p_{n-1}\\) .   \r\n\\(a_{n-1} = -(n-3)\\) \u3068\u306a\u308b\u306e\u306f, \u300cBH\u2026HB\u300d\u3068\u306a\u308b\u3068\u304d\u306e\u307f\u306a\u306e\u3067, \u305d\u306e\u78ba\u7387\u306f, \\(\\dfrac{1}{2^{n-1}}\\) .   \r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[ \\begin{align}\r\np_n & = \\dfrac{1}{2} p_{n-1} +\\dfrac{1}{2} \\cdot \\dfrac{1}{2^{n-1}} \\\\\r\n\\text{\u2234} \\quad 2^n p_n & = 2^{n-1} p_{n-1} +1\r\n\\end{align} \\]\r\n\u3088\u3063\u3066, \u3053\u308c\u3092\u7e70\u8fd4\u3057\u7528\u3044\u308c\u3070\r\n\\[ \\begin{align}\r\n2^n p_n & = ( n-3 ) +2^3 p_3 = n-1 \\\\\r\n\\text{\u2234} \\quad p_n & = \\dfrac{n-1}{2^n}\r\n\\end{align} \\]\r\n\u3053\u308c\u306f, \\(n = 3\\) \u306e\u3068\u304d\u3082\u307f\u305f\u3057\u3066\u3044\u308b.   \r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\underline{\\dfrac{n-1}{2^n}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u6570\u76f4\u7dda\u4e0a\u306e\u70b9P\u3092\u6b21\u306e\u898f\u5247\u3067\u79fb\u52d5\u3055\u305b\u308b. \u4e00\u679a\u306e\u786c\u8ca8\u3092\u6295\u3052\u3066, \u8868\u304c\u51fa\u308c\u3070P\u3092 \\(+1\\) \u3060\u3051\u79fb\u52d5\u3055\u305b, \u88cf\u304c\u51fa\u308c\u3070P\u3092\u539f\u70b9\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u306b\u79fb\u52d5\u3055\u305b\u308b. P\u306f\u521d\u3081\u539f\u70b9\u306b\u3042\u308b\u3068\u3057, \u786c\u8ca8\u3092 \\(n\\) \u56de\u6295\u3052\u305f\u5f8c\u306eP\u306e &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/htb201405\/\">\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":[124],"tags":[146,112],"class_list":["post-1217","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2014","tag-hitotsubashi","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1217","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=1217"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1217\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}