{"id":5213,"date":"2018-01-04T00:55:24","date_gmt":"2018-01-03T15:55:24","guid":{"rendered":"http:\/\/stuffy.dip.jp\/wordpress\/?p=5213"},"modified":"2022-05-13T06:21:27","modified_gmt":"2022-05-12T21:21:27","slug":"geometric-series","status":"publish","type":"post","link":"https:\/\/www.stuffy.site\/wordpress\/?p=5213","title":{"rendered":"\u7b49\u6bd4\u7d1a\u6570"},"content":{"rendered":"<p>\u6570\u5217{[pmath]a_{n}[\/pmath]}\u304c\u3001[pmath]a_{1}[\/pmath]=3, [pmath]a_{2}[\/pmath]=6,&nbsp;[pmath]a_{3}[\/pmath]=12, \u30fb\u30fb\u30fb,&nbsp;[pmath]a_{n}=3[\/pmath]\u30fb[pmath]2^{n-1}[\/pmath]\u3067\u8868\u3055\u308c\u308b\u3082\u306e\u3092\u521d\u9805\uff13\u3001\u516c\u6bd4\uff12\u306e\u7b49\u6bd4\u6570\u5217\u3068\u547c\u3073\u3001\u4e00\u822c\u306b\u521d\u9805a\u3001\u516c\u6bd4r\u3001\u306e\u7b49\u6bd4\u6570\u5217\u306f\u3001[pmath]a_{n}=ar^{n-1}[\/pmath]\u3068\u8868\u3055\u308c\u3001\u305d\u306e\u548c[pmath]S_{n}[\/pmath]\u3092\u7b49\u6bd4\u7d1a\u6570\u3068\u547c\u3073\u307e\u3059\u3002\u4eca\u3001\u8a66\u307f\u306b[pmath]S_{n}[\/pmath]\u3092\u6c42\u3081\u3066\u307f\u308b\u3068\u4e0b\u8a18\u3001\uff08\uff11\uff09\u5f0f\u306e\u4e21\u8fba\u306br \u3092\u304b\u3051\u305f\uff08\uff12\uff09\u5f0f\u3092\u7528\u610f\u3057\u3066<\/p>\n<p>[pmath]S_{n}[\/pmath]=[pmath]a[\/pmath]+[pmath]ar[\/pmath]+\u30fb\u30fb\u30fb\u30fb+[pmath]ar^{n-1}[\/pmath]\u3000\u3000\u3000\uff08\uff11\uff09<br \/>\n[pmath]rS_{n}[\/pmath]=&nbsp;&nbsp;&nbsp;&nbsp;[pmath]ar[\/pmath]+\u30fb\u30fb\u30fb\u30fb+[pmath]ar^{n-1}[\/pmath]+[pmath]ar^{n}[\/pmath]\u3000\u3000\u3000\uff08\uff12\uff09<\/p>\n<p>r\u22601 \u306e\u3068\u304d\u3001\uff08\uff11\uff09\u5f0f\u306e\u8fba\u3005\u304b\u3089\uff08\uff12\uff09\u3092\u5f15\u3044\u3066\uff08\uff11\uff09\uff0d\uff08\uff12\uff09\u3092\u8a08\u7b97\u3059\u308b\u3068\u3001<\/p>\n<p>[pmath](1-r)S_{n}=a-ar^{n}[\/pmath]<\/p>\n<p>[pmath]S_{n}={{a(1-r^{n})}\/{1-r}}={{a(r^{n}-1)}\/{r-1}}[\/pmath]\u3068\u516c\u5f0f\u3069\u304a\u308a\u6c42\u307e\u308a\u307e\u3057\u305f\u3002<\/p>\n<p>\u4eee\u306b\u4f8b\u3048\u3070\u5143\u91d1G\u3001\u5229\u606f\uff08\u6708\u5229\uff09r\u3001\u652f\u6255\u56de\u6570 n\u3001\u306e\u8eca\u306a\u308a\u30de\u30f3\u30b7\u30e7\u30f3\u3092\u8cb7\u3046\u3068\u304d\u3001\u30ed\u30fc\u30f3\u8fd4\u6e08\u3092\u7d44\u3080\u3068\u3001\u6708\u3005\u306e\u652f\u6255\u3044a\u306f\u3044\u304f\u3089\u306b\u306a\u308b\u3067\u3057\u3087\u3046\u304b\u3002<!--more--><\/p>\n<p>\u6bce\u6708\u3001\u5143\u91d1\u306b(1+r)\u306e\u5229\u606f\u3092\u639b\u3051\u3066\u6bce\u6708\u3001a\u306e\u652f\u6255\u3044\u3092n \u56de\u3057\u305f\u7d50\u679c\u3001\u6b8b\u91d1\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u3067\u3001<\/p>\n<p><a href=\"https:\/\/www.stuffy.site\/wordpress\/wp-content\/uploads\/2018\/01\/formula.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5231\" src=\"https:\/\/www.stuffy.site\/wordpress\/wp-content\/uploads\/2018\/01\/formula.png\" alt=\"\" width=\"590\" height=\"45\"><\/a><\/p>\n<p>\u6574\u7406\u3059\u308b\u3068\u3001<\/p>\n<p><a href=\"https:\/\/www.stuffy.site\/wordpress\/wp-content\/uploads\/2018\/01\/formula_.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5232\" src=\"https:\/\/www.stuffy.site\/wordpress\/wp-content\/uploads\/2018\/01\/formula_.png\" alt=\"\" width=\"601\" height=\"42\"><\/a><\/p>\n<p>\u5de6\u8fba\u306f\u521d\u9805a, \u516c\u6bd41+r \u306e\u7b49\u6bd4\u7d1a\u6570\u3067\u3059\u304b\u3089\u3001\u516c\u5f0f\u306b\u3088\u308a\u30fb\u30fb\u30fb<\/p>\n<p><a href=\"https:\/\/www.stuffy.site\/wordpress\/wp-content\/uploads\/2018\/01\/formula2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5233\" src=\"https:\/\/www.stuffy.site\/wordpress\/wp-content\/uploads\/2018\/01\/formula2.png\" alt=\"\" width=\"278\" height=\"83\"><\/a><\/p>\n<p>\u3057\u305f\u304c\u3063\u3066<\/p>\n<p><a href=\"https:\/\/www.stuffy.site\/wordpress\/wp-content\/uploads\/2018\/01\/formula3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5234\" src=\"https:\/\/www.stuffy.site\/wordpress\/wp-content\/uploads\/2018\/01\/formula3.png\" alt=\"\" width=\"235\" height=\"91\"><\/a><\/p>\n<p>\u652f\u6255\u3044\u7dcf\u984dG&#8217;=an\u3067\u3059\u306d\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u5217{[pmath]a_{n}[\/pmath]}\u304c\u3001[pmath]a_{1}[\/pmath]=3, [pmath]a_{2}[\/pmath]=6,&nbsp;[pmath]a_{3}[\/pmath]=12, \u30fb\u30fb\u30fb,&#038;n &hellip; <a href=\"https:\/\/www.stuffy.site\/wordpress\/?p=5213\" class=\"more-link\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"screen-reader-text\">\u7b49\u6bd4\u7d1a\u6570<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-5213","post","type-post","status-publish","format-standard","hentry","category-others"],"_links":{"self":[{"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/5213","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5213"}],"version-history":[{"count":2,"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/5213\/revisions"}],"predecessor-version":[{"id":7404,"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/5213\/revisions\/7404"}],"wp:attachment":[{"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.stuffy.site\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}