{"id":115,"date":"2011-11-28T00:03:31","date_gmt":"2011-11-27T15:03:31","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=115"},"modified":"2021-03-24T07:56:52","modified_gmt":"2021-03-23T22:56:52","slug":"kyr201006","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201006\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb\u4e592010\uff1a\u7b2c6\u554f"},"content":{"rendered":"
\n

\\(n\\) \u500b\u306e\u30dc\u30fc\u30eb\u3092 \\(2n\\) \u500b\u306e\u7bb1\u3078\u6295\u3052\u5165\u308c\u308b.\r\n\u5404\u30dc\u30fc\u30eb\u306f\u3044\u305a\u308c\u304b\u306e\u7bb1\u306b\u5165\u308b\u3082\u306e\u3068\u3057, \u3069\u306e\u7bb1\u306b\u5165\u308b\u78ba\u7387\u3082\u7b49\u3057\u3044\u3068\u3059\u308b.\r\n\u3069\u306e\u7bb1\u306b\u3082 \\(1\\) \u500b\u4ee5\u4e0b\u306e\u30dc\u30fc\u30eb\u3057\u304b\u5165\u3063\u3066\u3044\u306a\u3044\u78ba\u7387\u3092 \\(p _ n\\) \u3068\u3059\u308b.\r\n\u3053\u306e\u3068\u304d, \\(\\displaystyle\\lim _ {n \\rightarrow \\infty} \\dfrac{\\log p _ n}{n}\\) \u3092\u6c42\u3081\u3088.<\/p>\r\n

\r\n\r\n

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

\\[\\begin{align}\r\np _ n & = \\dfrac{{} _ {2n}\\text{P} {} _ n}{(2n)^n} \\\\\r\n& = \\dfrac{n}{2n} \\cdot \\dfrac{n+1}{2n} \\cdot \\cdots \\cdot \\dfrac{2n}{2n} \\\\\r\n& = \\dfrac{1}{2^n} \\textstyle\\prod\\limits _ {k=0}^n \\left( 1+\\dfrac{k}{n} \\right) \\\\\r\n\\text{\u2234} \\quad \\dfrac{\\log p _ n}{n} & = \\dfrac{1}{n} \\textstyle\\sum\\limits _ {k=0}^n \\log \\left( 1+\\dfrac{k}{n} \\right) -\\log2\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u533a\u5206\u6c42\u7a4d\u6cd5\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n\\displaystyle\\lim _ {n \\rightarrow \\infty}\\dfrac{\\log p _ n}{n} & = \\int _ 0^1 \\log (1+x) \\, dx -\\log 2 \\\\\r\n& = \\int _ 1^2 \\log x \\, dx -\\log 2 \\\\\r\n& = \\left[ x\\log x \\right] _ 1^2 -\\int _ 1^2 x \\cdot \\dfrac{1}{x} \\, dx -\\log 2 \\\\\r\n& = 2 \\log 2 -0 -\\left[ x \\right] _ 1^2 -\\log 2 \\\\\r\n& = \\underline{\\log 2 -1}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(n\\) \u500b\u306e\u30dc\u30fc\u30eb\u3092 \\(2n\\) \u500b\u306e\u7bb1\u3078\u6295\u3052\u5165\u308c\u308b. \u5404\u30dc\u30fc\u30eb\u306f\u3044\u305a\u308c\u304b\u306e\u7bb1\u306b\u5165\u308b\u3082\u306e\u3068\u3057, \u3069\u306e\u7bb1\u306b\u5165\u308b\u78ba\u7387\u3082\u7b49\u3057\u3044\u3068\u3059\u308b. \u3069\u306e\u7bb1\u306b\u3082 \\(1\\) \u500b\u4ee5\u4e0b\u306e\u30dc\u30fc\u30eb\u3057\u304b\u5165\u3063\u3066\u3044\u306a\u3044\u78ba\u7387\u3092 \\(p _ n\\) \u3068 … \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":[22],"tags":[140,14],"class_list":["post-115","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2010","tag-kyoto_r","tag-14"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/115","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=115"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/115\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=115"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=115"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}