{"id":129,"date":"2011-11-30T01:03:34","date_gmt":"2011-11-29T16:03:34","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=129"},"modified":"2021-09-24T18:05:18","modified_gmt":"2021-09-24T09:05:18","slug":"tok201003","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok201003\/","title":{"rendered":"\u6771\u5de5\u59272010\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\\(1\\) \u304b\u3089 \\(n\\) \u307e\u3067\u306e\u6570\u5b57\u304c\u3082\u308c\u306a\u304f\u4e00\u3064\u305a\u3064\u66f8\u304b\u308c\u305f \\(n\\) \u679a\u306e\u30ab\u30fc\u30c9\u306e\u675f\u304b\u3089\u540c\u6642\u306b \\(2\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u5f15\u304f.\r\n\u3053\u306e\u3068\u304d, \u5f15\u3044\u305f\u30ab\u30fc\u30c9\u306e\u6570\u5b57\u306e\u3046\u3061\u5c0f\u3055\u3044\u307b\u3046\u304c \\(3\\) \u306e\u500d\u6570\u3067\u3042\u308b\u78ba\u7387\u3092 \\(p(n)\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(p(8)\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u6b63\u306e\u6574\u6570 \\(k\\) \u306b\u5bfe\u3057, \\(p(3k+2)\\) \u3092 \\(k\\) \u3067\u8868\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u30ab\u30fc\u30c9\u304c \\(3k+2\\) \u679a\u3042\u308b\u3068\u304d, \\(2\\) \u679a\u3092\u5f15\u304f\u65b9\u6cd5\u306f\r\n\\[\r\n{} _ {3k+2} \\text{C} {} _ 2 = \\dfrac{1}{2}( 3k+2 )( 3k+1 ) \\ \\text{\u901a\u308a}\r\n\\]\r\n\u3053\u306e\u3046\u3061\u6761\u4ef6\u3092\u307f\u305f\u3059\u65b9\u6cd5\u306f, \\(1\\) \u679a\u306e\u30ab\u30fc\u30c9\u304c \\(3i \\ ( 1 \\leqq i \\leqq k )\\) \u3067\u3082\u3046 \\(1\\) \u679a\u306e\u30ab\u30fc\u30c9\u304c \\(3i+1\\) \u4ee5\u4e0a\u3067\u3042\u308b\u5834\u5408\u3067\u3042\u308b.
    \r\n\u3053\u306e\u65b9\u6cd5\u306f,\r\n\\[\\begin{align}\r\n\\textstyle\\sum\\limits _ {i=1}^k \\left\\{ ( 3k+2 ) -3i \\right\\} & = k( 3k+2 ) -3 \\cdot \\dfrac{1}{2} k( k+1 ) \\\\\r\n& = \\dfrac{1}{2} k \\left\\{ 2( 3k+2 ) -3( k+1 ) \\right\\} \\\\\r\n& = \\dfrac{1}{2} k ( 3k+1 ) \\ \\text{\u901a\u308a}\r\n\\end{align}\\]\r\n\u3086\u3048\u306b\r\n\\[\\begin{align}\r\np( 3k+2 ) & = \\dfrac{\\dfrac{1}{2} k ( 3k+1 )}{\\dfrac{1}{2}( 3k+2 )( 3k+1 )} \\\\\r\n& = \\underline{\\dfrac{k}{3k+2}}\r\n\\end{align}\\]\r\n

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

    (2)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\r\np(8) = \\dfrac{2}{3 \\cdot 2+2} = \\underline{\\dfrac{1}{4}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(1\\) \u304b\u3089 \\(n\\) \u307e\u3067\u306e\u6570\u5b57\u304c\u3082\u308c\u306a\u304f\u4e00\u3064\u305a\u3064\u66f8\u304b\u308c\u305f \\(n\\) \u679a\u306e\u30ab\u30fc\u30c9\u306e\u675f\u304b\u3089\u540c\u6642\u306b \\(2\\) \u679a\u306e\u30ab\u30fc\u30c9\u3092\u5f15\u304f. \u3053\u306e\u3068\u304d, \u5f15\u3044\u305f\u30ab\u30fc\u30c9\u306e\u6570\u5b57\u306e\u3046\u3061\u5c0f\u3055\u3044\u307b\u3046\u304c \\(3\\) \u306e\u500d\u6570\u3067\u3042\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":[25],"tags":[141,14],"class_list":["post-129","post","type-post","status-publish","format-standard","hentry","category-toko_2010","tag-toko","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/129","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=129"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/129\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=129"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}