{"id":5473,"date":"2026-04-09T10:00:32","date_gmt":"2026-04-09T01:00:32","guid":{"rendered":"https:\/\/winroadrikeijyuku.com\/oita\/?p=5473"},"modified":"2026-04-08T16:54:05","modified_gmt":"2026-04-08T07:54:05","slug":"%e6%95%b0%e5%88%97%e3%81%ae%e6%a5%b5%e9%99%90%e5%a4%a7%e9%98%aa%e5%a4%a72012-%e5%a4%a7%e5%88%86%e5%b8%82-%e5%a4%a7%e5%ad%a6%e5%8f%97%e9%a8%93-%e6%95%b0%e5%ad%a6-%e5%a1%be-%e5%a4%a7%e5%88%86","status":"publish","type":"post","link":"https:\/\/winroadrikeijyuku.com\/oita\/2026\/04\/09\/%e6%95%b0%e5%88%97%e3%81%ae%e6%a5%b5%e9%99%90%e5%a4%a7%e9%98%aa%e5%a4%a72012-%e5%a4%a7%e5%88%86%e5%b8%82-%e5%a4%a7%e5%ad%a6%e5%8f%97%e9%a8%93-%e6%95%b0%e5%ad%a6-%e5%a1%be-%e5%a4%a7%e5%88%86\/","title":{"rendered":"\u6570\u5217\u306e\u6975\u9650(\u5927\u962a\u59272012)| \u5927\u5206\u5e02 \u5927\u5b66\u53d7\u9a13 \u6570\u5b66 \u587e | \u5927\u5206\u7406\u7cfb\u5c02\u9580\u587eWINROAD"},"content":{"rendered":"

\u554f\u984c<\/p>\n

\u6570\u5217\u200b\\( \\{a_n\\} \\)<\/span>\u200b\u3092<\/p>\n

\u200b\\( a_1=1\u3001a_{n+1}=\\dfrac{na_n}{2+n(a_n+1)} \\)<\/span>\u200b\u306b\u3088\u3063\u3066\u5b9a\u3081\u308b\u3002<\/p>\n

(1) \u200b\\( a_2\u3001a_3\u3001a_4 \\)<\/span>\u200b\u3092\u6c42\u3081\u3088\u3002<\/p>\n

(2) \u4e00\u822c\u9805\u200b\\( a_n \\)<\/span>\u200b\u3092n\u3092\u7528\u3044\u3066\u8868\u305b\u3002<\/p>\n

(3) \u200b\\( \\displaystyle\\lim_{m\\to \\infty}m\\displaystyle\\sum_{n=m+1}^{2m}a_n \\)<\/span>\u200b\u3092\u6c42\u3081\u3088\u3002<\/p>\n

\n

(1) \u200b\\( a_2=\\dfrac{1\\cdot1}{2+1\\cdot(1+1)}=\\dfrac{1}{4} \\)<\/span>\u200b<\/span><\/p>\n

\u200b\\( a_3=\\dfrac{2\\cdot\\dfrac{1}{4}}{2+2\\cdot(\\dfrac{1}{4}+1)}=\\dfrac{1}{9} \\)<\/span>\u200b<\/span><\/p>\n

\u200b\\( a_4=\\dfrac{3\\cdot\\dfrac{1}{9}}{2+3\\cdot(\\dfrac{1}{9}+1)}=\\dfrac{1}{16} \\)<\/span>\u200b<\/span><\/p>\n

 <\/p>\n

(2) (1)\u3088\u308a\u200b\\( a_n=\\dfrac{1}{n^2} \\)<\/span>\u200b\u3068\u63a8\u5b9a\u3055\u308c\u308b\u3001\u3057\u305f\u304c\u3063\u3066\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u3067\u8a3c\u660e\u3057\u3066\u3044\u304f\u3002<\/span><\/p>\n

\u2460\u200b\\( n=1 \\)<\/span>\u200b\u306e\u3068\u304d<\/span><\/p>\n

\u200b\\( a_1=\\dfrac{1}{1^2}=1 \\)<\/span>\u200b\u3067\u6210\u7acb<\/span><\/p>\n

\u2461\u200b\\( n=k \\)<\/span>\u200b\u306e\u3068\u304d\u200b\\( a_k=\\dfrac{1}{k^2} \\)<\/span>\u200b\u304c\u6210\u7acb\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3002<\/span><\/p>\n

\u200b\\( n=k+1 \\)<\/span>\u200b\u306e\u3068\u304d<\/span><\/p>\n

\u200b\\( a_{k+1}\uff1d\\dfrac{ka_k}{2+k(a_k+1)}\\\\=\\dfrac{k\\cdot\\dfrac{1}{k^2}}{2+k(\\dfrac{1}{k^2}+1)}\\\\=\\dfrac{\\dfrac{1}{k}}{2+k(\\dfrac{1+k^2}{k^2})}\\\\=\\dfrac{1}{k^2+2k+1}=\\dfrac{1}{(k+1)^2} \\)<\/span>\u200b<\/span><\/p>\n

\u3068\u306a\u308a\u200b\\( n=k+1 \\)<\/span>\u200b\u306e\u3068\u304d\u3082\u6210\u7acb\u3002<\/span><\/p>\n

\u2460\u3001\u2461\u3088\u308a\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u3088\u308a\u200b\\( a_n=\\dfrac{1}{n^2} \\)<\/span>\u200b<\/span><\/p>\n

\n

(3) \u200b\\( \\displaystyle\\lim_{m\\to \\infty}m\\displaystyle\\sum_{n=m+1}^{2m}a_n\\\\=\\displaystyle\\lim_{m\\to \\infty}m\\displaystyle\\sum_{n=m+1}^{2m}\\dfrac{1}{n^2}\\\\=\\displaystyle\\lim_{m\\to \\infty}m\\displaystyle\\sum_{n=1}^{m}\\dfrac{1}{(n+m)^2}\\\\=\\displaystyle\\lim_{m\\to \\infty}\\dfrac{m^2}{m}\\displaystyle\\sum_{n=1}^{m}\\dfrac{1}{(n+m)^2}\\\\=\\displaystyle\\lim_{m\\to \\infty}\\dfrac{1}{m}\\displaystyle\\sum_{n=1}^{m}\\dfrac{m^2}{(n+m)^2}\\\\=\\displaystyle\\lim_{m\\to \\infty}\\dfrac{1}{m}\\displaystyle\\sum_{n=1}^{m}\\dfrac{1}{(\\dfrac{n}{m}+1)^2}=\\displaystyle\\int_0^1\\dfrac{1}{(x+1)^2}dx =\\dfrac{1}{2}\\)<\/span>\u200b<\/span><\/p>\n

\n

\uff08\u5927\u5206\u7406\u7cfb\u5c02\u9580\u587eWINROAD <\/span>\u9996\u85e4\uff09<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u554f\u984c \u6570\u5217\u200b\\( \\{a_n\\} \\)\u200b\u3092 \u200b\\( a_1=1\u3001a_{n+1}=\\dfrac{na_n}{2+n(a_n+1)} \\)\u200b\u306b\u3088\u3063\u3066\u5b9a\u3081\u308b\u3002 (1) \u200b\\( a_2\u3001a_3\u3001a_4 \\)\u200b\u3092\u6c42\u3081\u3088\u3002 (2) <\/p>\n

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"vkexunit_cta_each_option":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-5473","post","type-post","status-publish","format-standard","hentry","category-1"],"_links":{"self":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/5473","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/comments?post=5473"}],"version-history":[{"count":14,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/5473\/revisions"}],"predecessor-version":[{"id":5494,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/posts\/5473\/revisions\/5494"}],"wp:attachment":[{"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/media?parent=5473"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/categories?post=5473"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/winroadrikeijyuku.com\/oita\/wp-json\/wp\/v2\/tags?post=5473"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}