{"id":291,"date":"2012-02-04T00:43:09","date_gmt":"2012-02-03T15:43:09","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=291"},"modified":"2021-09-10T08:47:41","modified_gmt":"2021-09-09T23:47:41","slug":"osr200805","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr200805\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2008\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\\(1\\) \u679a\u306e\u786c\u8ca8\u3092\u7e70\u308a\u8fd4\u3057\u6295\u3052\u308b\u53cd\u5fa9\u8a66\u884c\u3092\u884c\u3044, \u8868\u304c \\(500\\) \u56de\u7d9a\u3051\u3066\u51fa\u305f\u3068\u304d\u306b\u7d42\u308f\u308b\u3082\u306e\u3068\u3059\u308b. \\(n\\) \u3092 \\(500\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u3068\u3059\u308b\u3068\u304d, \u3053\u306e\u53cd\u5fa9\u8a66\u884c\u304c \\(n\\) \u56de\u76ee\u3067\u7d42\u308f\u308b\u78ba\u7387\u3092 \\(p(n)\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(501 \\leqq n \\leqq 1000\\) \u306e\u3068\u304d, \\(p(n)\\) \u306f \\(n\\) \u306b\u95a2\u4fc2\u306a\u304f\u4e00\u5b9a\u306e\u5024\u306b\u306a\u308b\u3053\u3068\u3092\u793a\u3057, \u307e\u305f\u305d\u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(p(1002) -p(1001)\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(1002 \\leqq n \\leqq 1500\\) \u306e\u3068\u304d, \\(p(n+1) -p(n)\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \\(n\\) \u56de\u76ee\u3067\u8a66\u884c\u304c\u7d42\u308f\u308b\u306e\u306f, \u4ee5\u4e0b\u306e \\(3\\) \u3064\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3068\u304d\u3067\u3042\u308b.<\/p>\r\n

      \r\n

    1. (A)\u3000\\(1\\) \u56de\u76ee\u304b\u3089 \\(n-501\\) \u56de\u76ee\u307e\u3067\u306b, \u8868\u304c\u9023\u7d9a\u3057\u3066 \\(500\\) \u56de\u51fa\u3066\u3044\u306a\u3044.<\/p><\/li>\r\n

    2. (B)\u3000\\(n-500\\) \u56de\u76ee\u306b\u88cf\u304c\u51fa\u308b.<\/p><\/li>\r\n

    3. (C)\u3000\\(n-499\\) \u56de\u76ee\u304b\u3089 \\(n\\) \u56de\u76ee\u307e\u3067\u3059\u3079\u3066\u8868\u304c\u51fa\u308b.<\/p><\/li>\r\n<\/ol>\r\n

      \\(501 \\leqq n \\leqq 1000\\) \u306e\u3068\u304d, \\(1\\) \u56de\u76ee\u304b\u3089 \\(501-n\\) \u56de\u76ee\u307e\u3067\u306b \\(500\\) \u56de\u306e\u8a66\u884c\u304c\u884c\u308f\u308c\u306a\u3044\u306e\u3067, \u6761\u4ef6 (A) \u306f\u5fc5\u305a\u6e80\u305f\u3055\u308c\u308b.
      \r\n\u3088\u3063\u3066, \u6761\u4ef6 (B) \u3068 (C) \u3092\u307f\u305f\u305b\u3070\u3088\u304f, \\(p(n)\\) \u306f\u4e00\u5b9a\u306e\u5024\u306b\u306a\u308b.
      \r\n\u305d\u306e\u5024\u306f\r\n\\[\r\np(n) = \\dfrac{1}{2} \\left( \\dfrac{1}{2} \\right)^{500} = \\underline{\\dfrac{1}{2^{501}}}\n\\]\r\n

      (2)<\/strong><\/p>\r\n

      \\(n=500\\) \u306e\u3068\u304d\u306f, \u6761\u4ef6 (C) \u306e\u307f\u3092\u307f\u305f\u305b\u3070\u3088\u3044\u306e\u3067\r\n\\[\r\np(500) = \\left( \\dfrac{1}{2} \\right)^{500} = \\dfrac{1}{2^{500}}\n\\]\r\n\\(n=1001\\) \u306e\u3068\u304d, \\(1\\) \u56de\u76ee\u304b\u3089 \\(500\\) \u56de\u76ee\u307e\u3067\u306b\u8a66\u884c\u304c\u7d42\u308f\u308b\u78ba\u7387\u306f \\(p(500)\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\np(1001) & = \\left( 1 -p(500) \\right) \\cdot \\dfrac{1}{2} \\left( \\dfrac{1}{2} \\right)^{500} \\\\\r\n& = \\dfrac{1}{2^{501}} \\left( 1 -\\dfrac{1}{2^{500}} \\right)\n\\end{align}\\]\r\n\\(n=1002\\) \u306e\u3068\u304d, \\(1\\) \u56de\u76ee\u304b\u3089 \\(501\\) \u56de\u76ee\u307e\u3067\u306b\u8a66\u884c\u304c\u7d42\u308f\u308b\u78ba\u7387\u306f, \\(p(500) +p(501)\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\np(1002) & = \\left( 1 -p(500) -p(501) \\right) \\cdot \\dfrac{1}{2} \\left( \\dfrac{1}{2} \\right)^{500} \\\\\r\n& = \\dfrac{1}{2^{501}} \\left( 1 -\\dfrac{1}{2^{500}} -\\dfrac{1}{2^{501}}\\right)\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\np(1001) -p(1002) & = \\dfrac{1}{2^{501}} \\cdot \\dfrac{1}{2^{501}} \\\\\r\n& = \\underline{\\dfrac{1}{2^{1002}}}\n\\end{align}\\]\r\n

      (3)<\/strong><\/p>\r\n

      \\(1002 \\leqq n \\leqq 1501\\) \u306e\u3068\u304d, (2)<\/strong> \u3068\u540c\u69d8\u306b\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\r\n\\[\\begin{align}\r\np(n) & = \\left( 1 -\\textstyle\\sum\\limits _ {k=500}^{n-501} p(k) \\right) \\cdot \\dfrac{1}{2} \\left( \\dfrac{1}{2} \\right)^{500} \\\\\r\n& = \\dfrac{1}{2^{501}} \\left( 1 -\\dfrac{1}{2^{500}} -\\dfrac{n-1001}{2^{501}} \\right)\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\np(n+1) -p(n) & = \\dfrac{1}{2^{501}} \\cdot \\dfrac{1}{2^{501}} \\\\\r\n& = \\underline{\\dfrac{1}{2^{1002}}}\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(1\\) \u679a\u306e\u786c\u8ca8\u3092\u7e70\u308a\u8fd4\u3057\u6295\u3052\u308b\u53cd\u5fa9\u8a66\u884c\u3092\u884c\u3044, \u8868\u304c \\(500\\) \u56de\u7d9a\u3051\u3066\u51fa\u305f\u3068\u304d\u306b\u7d42\u308f\u308b\u3082\u306e\u3068\u3059\u308b. \\(n\\) \u3092 \\(500\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570\u3068\u3059\u308b\u3068\u304d, \u3053\u306e\u53cd\u5fa9\u8a66\u884c\u304c \\(n\\) \u56de\u76ee\u3067\u7d42\u308f\u308b\u78ba\u7387\u3092 … \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":[51],"tags":[142,16],"class_list":["post-291","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2008","tag-osaka_r","tag-16"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/291","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=291"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/291\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}