{"id":4326,"date":"2013-12-14T06:00:20","date_gmt":"2013-12-13T21:00:20","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4326"},"modified":"2014-09-10T16:51:23","modified_gmt":"2014-09-10T07:51:23","slug":"post-4326","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4326","title":{"rendered":"\u6570\u5217\u3068\u7d1a\u6570"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000\u6570\u5217\u306f\u81ea\u7136\u6570\u306e\u96c6\u5408\u306b\u57fa\u3044\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u95a2\u6570\u3067\u3042\u308a\uff0c\u6b21\u306e\u3088\u3046\u306b\u793a\u3055\u308c\u307e\u3059\uff0eu<sub>1<\/sub>, u<sub>2<\/sub>, &#8230; \u7565\u8a18\u3059\u308b\u3068 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clangle+u_n+%5Crangle&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\langle u_n \\rangle' title='\\langle u_n \\rangle' class='latex' \/> \u3068\u306a\u308a\u307e\u3059\uff0e\u4efb\u610f\u306e &epsilon; > 0 \u304c\u3042\u308a\uff0c\u3042\u308b\u6570 N > 0 \u304c\u5b58\u5728\u3057\uff0c|u<sub>n<\/sub> &#8211; l| < &epsilon; \u304c\u5168\u3066\u306e n > N \u306b\u3064\u3044\u3066\u6210\u308a\u7acb\u3064\u6642\uff0c\u3053\u306e\u6570\u5217\u306f\u6975\u9650\u5024 l \u3092\u6301\u3064\uff0c\u307e\u305f\u306f l \u306b\u53ce\u675f\u3059\u308b\u3068\u3044\u3044\u307e\u3059\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408\u306b\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clim%5Climits_%7Bn+%5Crightarrow+%5Cinfty%7D+u_n+%3Dl&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\lim\\limits_{n \\rightarrow \\infty} u_n =l' title='\\lim\\limits_{n \\rightarrow \\infty} u_n =l' class='latex' \/> \u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0e\u6570\u5217\u304c\u53ce\u675f\u3057\u306a\u3044\u5834\u5408\u306f\u767a\u6563\u3059\u308b\u3068\u3044\u3044\u307e\u3059\uff0e<\/p>\n<p>\u3000\u6b21\u306e\u3088\u3046\u306a\u6570\u5217\u3092\u8003\u3048\u3066\u307f\u307e\u3059\uff0e u<sub>1<\/sub>, u<sub>1<\/sub> + u<sub>2<\/sub>, u<sub>1<\/sub> + u<sub>2<\/sub> + u<sub>3<\/sub>, &#8230; \u307e\u305f\u306f S<sub>1<\/sub>, S<sub>2<\/sub>, S<sub>3<\/sub>, &#8230; \u305f\u3060\u3057 S<sub>n<\/sub> = u<sub>1<\/sub> + u<sub>2<\/sub> + &#8230; + u<sub>n<\/sub>\uff0e\u3053\u308c\u3092 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clangle+S_n+%5Crangle&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\langle S_n \\rangle' title='\\langle S_n \\rangle' class='latex' \/> \u3068\u8a18\u8ff0\u3057\uff0c\u6570\u5217 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clangle+u_n+%5Crangle&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\langle u_n \\rangle' title='\\langle u_n \\rangle' class='latex' \/> \u306e\u90e8\u5206\u548c\u306e\u6570\u5217\u3068\u547c\u3073\u307e\u3059\uff0e\u305d\u306e\u8a18\u53f7\u306f<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+u_1+%2B+u_2+%2B+u_3+%2B+%5Ccdots+&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle u_1 + u_2 + u_3 + \\cdots ' title='\\displaystyle u_1 + u_2 + u_3 + \\cdots ' class='latex' \/> \u307e\u305f\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7Du_n&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\sum_{n=1}^{\\infty}u_n' title='\\displaystyle \\sum_{n=1}^{\\infty}u_n' class='latex' \/> \u307e\u305f\u306f\u7565\u8a18\u3057\u3066 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Csum+u_n&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\sum u_n' title='\\displaystyle \\sum u_n' class='latex' \/><\/p>\n<p>\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\uff0c<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clangle+S_n+%5Crangle&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\langle S_n \\rangle' title='\\langle S_n \\rangle' class='latex' \/> \u3068\u540c\u7fa9\u3067\u3042\u308a\u7121\u9650\u7d1a\u6570\u3068\u547c\u3073\u307e\u3059\uff0e\u3053\u306e\u7d1a\u6570\u304c\u53ce\u675f\u3059\u308b\u304b\u767a\u6563\u3059\u308b\u304b\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Clangle+S_n+%5Crangle&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\langle S_n \\rangle' title='\\langle S_n \\rangle' class='latex' \/> \u304c\u53ce\u675f\u3059\u308b\u304b\u767a\u6563\u3059\u308b\u304b\u306b\u4f9d\u5b58\u3057\u307e\u3059\uff0eS \u306b\u53ce\u675f\u3059\u308b\u306a\u3089 S \u306f\u6570\u5217\u306e\u5408\u8a08\u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n<p>\u3000\u4ee5\u4e0b\u306f\u7121\u9650\u7d1a\u6570\u306b\u3064\u3044\u3066\u306e\u3044\u304f\u3064\u304b\u306e\u91cd\u8981\u306a\u5b9a\u7406\u3067\u3059\uff0e<\/p>\n<ol>\n<li>\u7d1a\u6570 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Csum_%7Bn%3D1%7D%5E%7B%5Cinfty%7D%5Cfrac%7B1%7D%7Bn%5Ep%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\sum_{n=1}^{\\infty}\\frac{1}{n^p}' title='\\displaystyle \\sum_{n=1}^{\\infty}\\frac{1}{n^p}' class='latex' \/> \u306f p > 1 \u306a\u3089\u53ce\u675f\u3057\uff0c p &le; 1 \u306a\u3089\u767a\u6563\u3059\u308b\uff0e<\/li>\n<li>&sum;|u<sub>n<\/sub>| \u304c\u53ce\u675f\u3057\u304b\u3064 |v<sub>n<\/sub>| &le; |u<sub>n<\/sub>| \u306a\u3089 &sum;|v<sub>n<\/sub>| \u306f\u53ce\u675f\u3059\u308b\uff0e<\/li>\n<li>&sum;|u<sub>n<\/sub>| \u304c\u53ce\u675f\u3059\u308b\u306a\u3089 &sum;u<sub>n<\/sub> \u306f\u53ce\u675f\u3059\u308b\uff0e<\/li>\n<li>&sum;|u<sub>n<\/sub>| \u304c\u767a\u6563\u3057\u304b\u3064 v<sub>n<\/sub> &ge; |u<sub>n<\/sub>| \u306a\u3089 &sum;v<sub>n<\/sub> \u306f\u767a\u6563\u3059\u308b\uff0e<\/li>\n<li>\u7d1a\u6570 &sum;|u<sub>n<\/sub>| \u305f\u3060\u3057 |u<sub>n<\/sub>| = f(n) &ge; 0 \u304c\u53ce\u675f\u3059\u308b\u304b\u767a\u6563\u3059\u308b\u304b\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cint_%7B1%7D%5E%7B%5Cinfty%7Df%28x%29dx+%3D+%5Clim%5Climits_%7BM+%5Crightarrow+%5Cinfty%7D%5Cint_%7B1%7D%5E%7BM%7Df%28x%29dx&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\int_{1}^{\\infty}f(x)dx = \\lim\\limits_{M \\rightarrow \\infty}\\int_{1}^{M}f(x)dx' title='\\displaystyle \\int_{1}^{\\infty}f(x)dx = \\lim\\limits_{M \\rightarrow \\infty}\\int_{1}^{M}f(x)dx' class='latex' \/> \u304c\u5b58\u5728\u3059\u308b\u304b\u3057\u306a\u3044\u304b\u306b\u4f9d\u5b58\u3059\u308b\uff0e\u3053\u306e\u5b9a\u7406\u306f\u3057\u3070\u3057\u3070\u7a4d\u5206\u5224\u5b9a\u6cd5\u3068\u547c\u3070\u308c\u308b\uff0e<\/li>\n<li>\u7d1a\u6570 &sum;|u<sub>n<\/sub>| \u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Clim%5Climits_%7Bn+%5Crightarrow+%5Cinfty%7D%7Cu_n%7C+%5Cneq+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\lim\\limits_{n \\rightarrow \\infty}|u_n| \\neq 0' title='\\displaystyle \\lim\\limits_{n \\rightarrow \\infty}|u_n| \\neq 0' class='latex' \/> \u306a\u3089\u767a\u6563\u3059\u308b\uff0e\u3057\u304b\u3057\u306a\u304c\u3089\uff0c\u4eee\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Clim%5Climits_%7Bn+%5Crightarrow+%5Cinfty%7D%7Cu_n%7C+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\lim\\limits_{n \\rightarrow \\infty}|u_n| = 0' title='\\displaystyle \\lim\\limits_{n \\rightarrow \\infty}|u_n| = 0' class='latex' \/> \u306e\u5834\u5408\uff0c\u7d1a\u6570\u304c\u53ce\u675f\u3059\u308b\u304b\u767a\u6563\u3059\u308b\u304b\u306f\u5206\u304b\u3089\u306a\u3044\uff0e<\/li>\n<li>\u6b21\u306e\u3088\u3046\u306b\u4eee\u5b9a\u3057\u3066\u307f\u308b\uff0e<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Clim%5Climits_%7Bn+%5Crightarrow+%5Cinfty%7D%5Cleft%7C%5Cfrac%7Bu_%7Bn%2B1%7D%7D%7Bn_n%7D%5Cright%7C+%3D+r&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\lim\\limits_{n \\rightarrow \\infty}\\left|\\frac{u_{n+1}}{n_n}\\right| = r' title='\\displaystyle \\lim\\limits_{n \\rightarrow \\infty}\\left|\\frac{u_{n+1}}{n_n}\\right| = r' class='latex' \/>. \u3059\u308b\u3068\u7d1a\u6570 &sum;u<sub>n<\/sub> converges (absolutely) \u306f r < 1 \u306a\u3089\u53ce\u675f\u3057\uff0c r > 1 \u306a\u3089\u767a\u6563\u3059\u308b\uff0er = 1 \u306e\u5834\u5408\u7d50\u8ad6\u306f\u4e00\u5b9a\u3067\u306f\u306a\u3044\uff0e\u3053\u306e\u5b9a\u7406\u306f\u3057\u3070\u3057\u3070\u6bd4\u5224\u5b9a\u6cd5\u3068\u3057\u3066\u5f15\u7528\u3055\u308c\u308b\uff0e<\/li>\n<\/ol>\n<p><iframe src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=fujiitoshiki-22&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=ss_til&#038;asins=0071635408\" style=\"width:120px;height:240px;\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000\u6570\u5217\u306f\u81ea\u7136\u6570\u306e\u96c6\u5408\u306b\u57fa\u3044\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u95a2\u6570\u3067\u3042\u308a\uff0c\u6b21\u306e\u3088\u3046\u306b\u793a\u3055\u308c\u307e\u3059\uff0eu1, u2, &#8230; \u7565\u8a18\u3059\u308b\u3068 \u3068\u306a\u308a\u307e\u3059\uff0e\u4efb\u610f\u306e &epsilon; > 0 \u304c\u3042\u308a\uff0c\u3042\u308b\u6570 N > 0 \u304c\u5b58\u5728\u3057\uff0c|un &#038;#821 &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4326\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u6570\u5217\u3068\u7d1a\u6570&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4326","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4326","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4326"}],"version-history":[{"count":13,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4326\/revisions"}],"predecessor-version":[{"id":6809,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4326\/revisions\/6809"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}