{"id":1036,"date":"2015-04-10T23:35:16","date_gmt":"2015-04-10T14:35:16","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1036"},"modified":"2021-10-31T06:40:39","modified_gmt":"2021-10-30T21:40:39","slug":"tkb201304","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201304\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2013\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

A , B \u306e \\(2\\) \u4eba\u304c\u3044\u308b.\r\n\u6295\u3052\u305f\u3068\u304d\u8868\u88cf\u306e\u51fa\u308b\u78ba\u7387\u304c\u305d\u308c\u305e\u308c \\(\\dfrac{1}{2}\\) \u306e\u30b3\u30a4\u30f3\u304c \\(1\\) \u679a\u3042\u308a, \u6700\u521d\u306f A \u304c\u305d\u306e\u30b3\u30a4\u30f3\u3092\u6301\u3063\u3066\u3044\u308b. \u6b21\u306e\u64cd\u4f5c\u3092\u7e70\u308a\u8fd4\u3059.<\/p>\r\n

    \r\n

  1. (i)\u3000A \u304c\u30b3\u30a4\u30f3\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u304d\u306f, \u30b3\u30a4\u30f3\u3092\u6295\u3052, \u8868\u304c\u51fa\u308c\u3070 A \u306b \\(1\\) \u70b9\u3092\u4e0e\u3048, \u30b3\u30a4\u30f3\u306f A \u304c\u305d\u306e\u307e\u307e\u6301\u3064. \u88cf\u304c\u51fa\u308c\u3070, \u4e21\u8005\u306b\u70b9\u3092\u4e0e\u3048\u305a, A \u306f\u30b3\u30a4\u30f3\u3092 B \u306b\u6e21\u3059.<\/p><\/li>\r\n

  2. (ii)\u3000B \u304c\u30b3\u30a4\u30f3\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u304d\u306f, \u30b3\u30a4\u30f3\u3092\u6295\u3052, \u8868\u304c\u51fa\u308c\u3070 B \u306b \\(1\\) \u70b9\u3092\u4e0e\u3048, \u30b3\u30a4\u30f3\u306f B \u304c\u305d\u306e\u307e\u307e\u6301\u3064. \u88cf\u304c\u51fa\u308c\u3070, \u4e21\u8005\u306b\u70b9\u3092\u4e0e\u3048\u305a, B \u306f\u30b3\u30a4\u30f3\u3092 A \u306b\u6e21\u3059.<\/p><\/li>\r\n<\/ol>\r\n

    \u305d\u3057\u3066 A , B \u306e\u3044\u305a\u308c\u304b\u304c \\(2\\) \u70b9\u3092\u7372\u5f97\u3057\u305f\u6642\u70b9\u3067, \\(2\\) \u70b9\u3092\u7372\u5f97\u3057\u305f\u65b9\u306e\u52dd\u5229\u3068\u3059\u308b. \u305f\u3068\u3048\u3070, \u30b3\u30a4\u30f3\u304c\u8868, \u88cf, \u8868, \u8868\u3068\u51fa\u305f\u5834\u5408, \u3053\u306e\u6642\u70b9\u3067 A \u306f \\(1\\) \u70b9, B \u306f \\(2\\) \u70b9\u3092\u7372\u5f97\u3057\u3066\u3044\u308b\u306e\u3067, B \u306e\u52dd\u5229\u3068\u306a\u308b.\r\nA , B \u3042\u308f\u305b\u3066\u3061\u3087\u3046\u3069 \\(n\\) \u56de\u30b3\u30a4\u30f3\u3092\u6295\u3052\u7d42\u3048\u305f\u3068\u304d\u306b A \u306e\u52dd\u5229\u3068\u306a\u308b\u78ba\u7387 \\(p _ n\\) \u3092\u6c42\u3081\u3088.<\/p>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n
      \r\n

    1. 1*<\/strong>\u3000\\(n=1\\) \u306e\u3068\u304d
      \r\n\u52dd\u6557\u304c\u3064\u304f\u3053\u3068\u306f\u306a\u3044\u306e\u3067\r\n\\[\r\np _ 1 = 0\r\n\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\(n=2\\) \u306e\u3068\u304d
      \r\n\u300c\u8868\u8868\u300d\u3068\u51fa\u308c\u3070, A \u304c\u52dd\u3064\u306e\u3067\r\n\\[\r\np _ 2 = \\dfrac{1}{2} \\cdot \\dfrac{1}{2} = \\dfrac{1}{4}\r\n\\]<\/li>\r\n

    3. 3*<\/strong>\u3000\\(n=3\\) \u306e\u3068\u304d
      \r\nA \u304c\u52dd\u3064\u3053\u3068\u306f\u306a\u3044\u306e\u3067\r\n\\[\r\np _ 3 = 0\r\n\\]<\/li>\r\n

    4. 4*<\/strong>\u3000\\(n\\) \u304c \\(4\\) \u4ee5\u4e0a\u306e\u5076\u6570\u306e\u3068\u304d
      \r\n\\(1\\) \u56de\u76ee\u304b\u3089 \\(n-1\\) \u56de\u76ee\u307e\u3067\u306b, \u300c\u8868\u300d\u304c \\(1\\) \u56de, \u300c\u88cf\u8868\u300d\u306e\u7d44\u304c \\(\\dfrac{n-2}{2}\\) \u56de\u51fa\u3066, \\(n\\) \u56de\u76ee\u306b\u300c\u8868\u300d\u304c\u51fa\u308c\u3070, A \u304c\u52dd\u3064\u306e\u3067\r\n\\[\r\np _ n = \\dfrac{n}{2} \\cdot \\left( \\dfrac{1}{2} \\right)^n = \\dfrac{n}{2^{n+1}}\r\n\\]\r\n\u3053\u308c\u306f, \\(n=2\\) \u306e\u3068\u304d\u3082\u6e80\u305f\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n

    5. 5*<\/strong>\u3000\\(n\\) \u304c \\(4\\) \u4ee5\u4e0a\u306e\u5947\u6570\u306e\u3068\u304d
      \r\n\\(1\\) \u56de\u76ee\u304b\u3089 \\(n-1\\) \u56de\u76ee\u307e\u3067\u306b, \u300c\u8868\u300d\u304c \\(1\\) \u56de, \u300c\u88cf\u88cf\u8868\u300d\u306e\u7d44\u304c \\(1\\) \u56de, \u300c\u88cf\u8868\u300d\u306e\u7d44\u304c \\(\\dfrac{n-5}{2}\\) \u56de\u51fa\u3066, \\(n\\) \u56de\u76ee\u306b\u300c\u8868\u300d\u304c\u51fa\u308c\u3070, A \u304c\u52dd\u3064\u306e\u3067\r\n\\[\\begin{align}\r\np _ n & = \\dfrac{n-1}{2} \\cdot \\dfrac{n-3}{2} \\cdot \\left( \\dfrac{1}{2} \\right)^n \\\\\r\n& = \\dfrac{(n-1)(n-3)}{2^{n+2}}\r\n\\end{align}\\]\r\n\u3053\u308c\u306f, \\(n=1, 3\\) \u306e\u3068\u304d\u3082\u6e80\u305f\u3057\u3066\u3044\u308b.<\/p><\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b\u78ba\u7387 \\(p _ n\\) \u306f\r\n\\[\r\np _ n = \\underline{\\left\\{\\begin{array}{ll} \\dfrac{n}{2^{n+1}} & \\left( n \\text{\u304c\u5076\u6570\u306e\u3068\u304d} \\right) \\\\ \\dfrac{(n-1)(n-3)}{2^{n+2}} & \\left( n \\text{\u304c\u5947\u6570\u306e\u3068\u304d} \\right) \\end{array}\\right.}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"A , B \u306e \\(2\\) \u4eba\u304c\u3044\u308b. \u6295\u3052\u305f\u3068\u304d\u8868\u88cf\u306e\u51fa\u308b\u78ba\u7387\u304c\u305d\u308c\u305e\u308c \\(\\dfrac{1}{2}\\) \u306e\u30b3\u30a4\u30f3\u304c \\(1\\) \u679a\u3042\u308a, \u6700\u521d\u306f A \u304c\u305d\u306e\u30b3\u30a4\u30f3\u3092\u6301\u3063\u3066\u3044\u308b. \u6b21\u306e\u64cd\u4f5c\u3092\u7e70\u308a\u8fd4\u3059. (i)\u3000A \u304c … \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":[106],"tags":[149,111],"class_list":["post-1036","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2013","tag-tokyo_b","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1036","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=1036"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1036\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1036"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1036"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1036"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}