{"id":1377,"date":"2017-02-17T21:51:50","date_gmt":"2017-02-17T12:51:50","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1377"},"modified":"2021-10-26T08:07:17","modified_gmt":"2021-10-25T23:07:17","slug":"tkr201602","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr201602\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2016\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>A , B , C \u306e \\(3\\) \u3064\u306e\u30c1\u30fc\u30e0\u304c\u53c2\u52a0\u3059\u308b\u91ce\u7403\u306e\u5927\u4f1a\u3092\u958b\u50ac\u3059\u308b.\r\n\u4ee5\u4e0b\u306e\u65b9\u5f0f\u3067\u8a66\u5408\u3092\u884c\u3044, \\(2\\) \u9023\u52dd\u3057\u305f\u30c1\u30fc\u30e0\u304c\u51fa\u305f\u6642\u70b9\u3067, \u305d\u306e\u30c1\u30fc\u30e0\u3092\u512a\u52dd\u30c1\u30fc\u30e0\u3068\u3057\u3066\u5927\u4f1a\u306f\u7d42\u4e86\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(a)<\/strong>\u3000\\(1\\) \u8a66\u5408\u76ee\u3067 A \u3068 B \u304c\u5bfe\u6226\u3059\u308b.<\/p><\/li>\r\n<li><p><strong>(b)<\/strong>\u3000\\(2\\) \u8a66\u5408\u76ee\u3067, \\(1\\) \u8a66\u5408\u76ee\u306e\u52dd\u8005\u3068, \\(1\\) \u8a66\u5408\u76ee\u3067\u5f85\u6a5f\u3057\u3066\u3044\u305f C \u304c\u5bfe\u6226\u3059\u308b.<\/p><\/li>\r\n<li><p><strong>(c)<\/strong>\u3000\\(k\\) \u8a66\u5408\u76ee\u3067\u512a\u52dd\u30c1\u30fc\u30e0\u304c\u6c7a\u307e\u3089\u306a\u3044\u5834\u5408\u306f, \\(k\\) \u8a66\u5408\u76ee\u306e\u52dd\u8005\u3068 \\(k\\) \u8a66\u5408\u76ee\u3067\u5f85\u6a5f\u3057\u3066\u3044\u305f\u30c1\u30fc\u30e0\u304c \\(k+1\\) \u8a66\u5408\u76ee\u3067\u5bfe\u6226\u3059\u308b. \u3053\u3053\u3067 \\(k\\) \u306f \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b.<\/p><\/li>\r\n<\/ol>\r\n<p>\u306a\u304a, \u3059\u3079\u3066\u306e\u5bfe\u6226\u306b\u304a\u3044\u3066, \u305d\u308c\u305e\u308c\u306e\u30c1\u30fc\u30e0\u304c\u52dd\u3064\u78ba\u7387\u306f \\(\\dfrac{1}{2}\\) \u3067, \u5f15\u304d\u5206\u3051\u306f\u306a\u3044\u3082\u306e\u3068\u3059\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3059\u308b. \u3061\u3087\u3046\u3069 \\(n\\) \u8a66\u5408\u76ee\u3067 A \u304c\u512a\u52dd\u3059\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(m\\) \u3092\u6b63\u306e\u6574\u6570\u3068\u3059\u308b. \u7dcf\u8a66\u5408\u6570\u304c \\(3m\\) \u56de\u4ee5\u4e0b\u3067 A \u304c\u512a\u52dd\u3057\u305f\u3068\u304d, A \u306e\u6700\u5f8c\u306e\u5bfe\u6226\u76f8\u624b\u304c B \u3067\u3042\u308b\u6761\u4ef6\u4ed8\u304d\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>A \u304c\u512a\u52dd\u3059\u308b\u306e\u306f, \u6b21\u306e \\(2\\) \u901a\u308a\u304c\u8003\u3048\u3089\u308c\u308b.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\u4ee5\u4e0b\u306e \\(3\\) \u8a66\u5408\u306e\u30bb\u30c3\u30c8\u304c \\(0\\) \u56de\u4ee5\u4e0a\u7e70\u308a\u8fd4\u3055\u308c\u305f\u5f8c\u306b, A \u304c B , C \u306b\u9023\u52dd\u3059\u308b.\r\n<ul>\r\n<li><p>A \u5bfe B \u3067 A \u304c\u52dd\u3064<\/p><\/li>\r\n<li><p>A \u5bfe C \u3067 C \u304c\u52dd\u3064<\/p><\/li>\r\n<li><p>B \u5bfe C \u3067 B \u304c\u52dd\u3064<\/p><\/li>\r\n<\/ul>\r\n\u3053\u306e\u3068\u304d, A \u304c \\(n = 3m-1 \\ ( m \\geqq 1 )\\) \u8a66\u5408\u76ee\u3067\u512a\u52dd\u3057, \u305d\u306e\u78ba\u7387\u306f\r\n\\[\r\n\\left( \\dfrac{1}{8} \\right)^{m-1} \\cdot \\dfrac{1}{4} = \\left( \\dfrac{1}{2} \\right)^{3m-1} = \\left( \\dfrac{1}{2} \\right)^n\r\n\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\u4ee5\u4e0b\u306e \\(3\\) \u8a66\u5408\u306e\u30bb\u30c3\u30c8\u304c \\(1\\) \u56de\u4ee5\u4e0a\u7e70\u308a\u8fd4\u3055\u308c\u305f\u5f8c\u306b, A \u304c B \u306b\u52dd\u3064.\r\n<ul>\r\n<li><p>A \u5bfe B \u3067 B \u304c\u52dd\u3064<\/p><\/li>\r\n<li><p>B \u5bfe C \u3067 C \u304c\u52dd\u3064<\/p><\/li>\r\n<li><p>A \u5bfe C \u3067 A \u304c\u52dd\u3064<\/p><\/li>\r\n<\/ul>\r\n\u3053\u306e\u3068\u304d, A \u304c \\(n = 3m+1 \\ ( m \\geqq 1 )\\) \u8a66\u5408\u76ee\u3067\u512a\u52dd\u3057, \u305d\u306e\u78ba\u7387\u306f\r\n\\[\r\n\\left( \\dfrac{1}{8} \\right)^m \\cdot \\dfrac{1}{2} = \\left( \\dfrac{1}{2} \\right)^{3m+1} = \\left( \\dfrac{1}{2} \\right)^n\r\n\\]<\/li>\r\n<\/ol>\r\n<p>\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\r\n\\underline{\\left\\{ \\begin{array}{ll} 0 & ( \\ n \\ \\text{\u304c} \\ 3 \\ \\text{\u306e\u500d\u6570\u306e\u3068\u304d} \\ ) \\\\ \\left( \\dfrac{1}{2} \\right)^n & ( \\ n \\ \\text{\u304c} \\ 3 \\ \\text{\u306e\u500d\u6570\u3067\u306a\u3044\u3068\u304d} \\ ) \\end{array} \\right.}\r\n\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong> \u306e\u5834\u5408, \u3064\u307e\u308a A \u304c C \u306b\u52dd\u3063\u3066\u512a\u52dd\u3059\u308b\u3068\u304d<br \/>\r\n\u3053\u306e\u78ba\u7387\u3092 \\(p _ m\\) \u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\np _ m & = \\textstyle\\sum\\limits _ {k=1}^{m} \\left( \\dfrac{1}{2} \\right)^{3k-1} = \\dfrac{1}{4} \\cdot \\dfrac{1 -\\left( \\dfrac{1}{8} \\right)^m}{1 -\\dfrac{1}{8}} \\\\\r\n& = \\dfrac{2}{7} \\cdot \\dfrac{8^m -1}{8^m}\r\n\\end{align}\\]<\/li>\r\n<li><p><strong>2*<\/strong> \u306e\u5834\u5408, \u3064\u307e\u308a A \u304c B \u306b\u52dd\u3063\u3066\u512a\u52dd\u3059\u308b\u3068\u304d<br \/>\r\n\u3053\u306e\u78ba\u7387\u3092 \\(q _ m\\) \u3068\u304a\u3051\u3070\r\n\\[\\begin{align}\r\nq _ m & = \\textstyle\\sum\\limits _ {k=1}^{m-1} \\left( \\dfrac{1}{2} \\right)^{3k+1} \\\\\r\n& = \\dfrac{1}{16} \\cdot \\dfrac{1 -\\left( \\dfrac{1}{8} \\right)^{m-1}}{1 -\\dfrac{1}{8}} = \\dfrac{1}{14} \\cdot \\dfrac{8^m -8}{8^m}\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n<p>\u3053\u3053\u3067\r\n\\[\r\n\\dfrac{p _ m}{q _ m} = \\dfrac{\\dfrac{2}{7} \\cdot \\dfrac{8^m -1}{8^m}}{\\dfrac{1}{14} \\cdot \\dfrac{8^m -8}{8^m}} = \\dfrac{4 \\cdot 8^m -4}{8^m -8}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\\begin{align}\r\n\\dfrac{q _ m}{p _ m +q _ m} & = \\dfrac{1}{\\dfrac{p _ m}{q _ m} +1} \\\\\r\n& = \\dfrac{8^m -8}{4 \\cdot 8^m -4 +8^m -8} \\\\\r\n& = \\underline{\\dfrac{8^m -8}{5 \\cdot 8^m -12}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"A , B , C \u306e \\(3\\) \u3064\u306e\u30c1\u30fc\u30e0\u304c\u53c2\u52a0\u3059\u308b\u91ce\u7403\u306e\u5927\u4f1a\u3092\u958b\u50ac\u3059\u308b. \u4ee5\u4e0b\u306e\u65b9\u5f0f\u3067\u8a66\u5408\u3092\u884c\u3044, \\(2\\) \u9023\u52dd\u3057\u305f\u30c1\u30fc\u30e0\u304c\u51fa\u305f\u6642\u70b9\u3067, \u305d\u306e\u30c1\u30fc\u30e0\u3092\u512a\u52dd\u30c1\u30fc\u30e0\u3068\u3057\u3066\u5927\u4f1a\u306f\u7d42\u4e86\u3059\u308b. (a)\u3000\\(1\\) \u8a66\u5408\u76ee &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tkr201602\/\">\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":[150],"tags":[139,162],"class_list":["post-1377","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2016","tag-tokyo_r","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1377","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=1377"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1377\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}