{"id":6649,"date":"2021-07-20T23:18:56","date_gmt":"2021-07-20T14:18:56","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6649"},"modified":"2021-08-03T02:00:22","modified_gmt":"2021-08-02T17:00:22","slug":"definition-of-a-sequence","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/definition-of-a-sequence\/","title":{"rendered":"\uc218\uc5f4\uc758 \uc815\uc758"},"content":{"rendered":"<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 1\uc7a5 1\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; <span class=\"itc_viewcontents\">(<a href=\"..\/\">\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30<\/a>)<\/span><\/p>\n<\/div>\n<p><span class=\"defined\">\uc218\uc5f4<\/span>(sequence)\uc774\ub780, \uc9c1\uad00\uc801\uc73c\ub85c \uc815\uc758\ud558\uc790\uba74,<br \/>\n\\[a_1 ,\\, a_2 ,\\, a_3 ,\\, \\cdots\\]<br \/>\n\uacfc \uac19\uc774 \uc218\ub97c \ud55c \uc904\ub85c \ub098\uc5f4\ud55c \uac83\uc774\ub2e4. \uc218\uc5f4\uc744 \uc774\ub8e8\uace0 \uc788\ub294 \uac01 \uc218\ub97c <span class=\"defined\">\ud56d<\/span>(term)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \ud56d \\(a_n\\)\uc744 <span class=\"defined\">\\(\\boldsymbol{n}\\)\uc9f8 \ud56d<\/span>\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \ud56d\uc758 \uc218\uac00 \uc720\ud55c\uc778 \uc218\uc5f4\uc744 <span class=\"defined\">\uc720\ud55c\uc218\uc5f4<\/span>(finite sequence)\uc774\ub77c\uace0 \ubd80\ub974\uace0, \ud56d\uc758 \uc218\uac00 \ubb34\ud55c\uc778 \uc218\uc5f4\uc744 <span class=\"defined\">\ubb34\ud55c\uc218\uc5f4<\/span>(infinite sequence)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc218\uc5f4<br \/>\n\\[a_1 ,\\, a_2 ,\\, a_3 ,\\, \\cdots\\]<br \/>\n\uc744 \uac04\ub2e8\ud788 \\(\\left\\{ a_n \\right\\}\\) \ub610\ub294 \\(\\left( a_n \\right)\\)\uacfc \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\ud568\uc218\uc758 \uac1c\ub150\uc744 \uc0ac\uc6a9\ud558\uc5ec \ubb34\ud55c\uc218\uc5f4\uc744 \uc815\uc758\ud560 \uc218 \uc788\ub2e4. \\(n_0\\)\uac00 \uc815\uc218\uc77c \ub54c \uc9d1\ud569 \\(Z_{n_0}\\)\ub97c<br \/>\n\\[Z_{n_0} = \\left\\{ n\\in\\mathbb{Z} \\,\\vert\\, n\\ge n_0 \\right\\}\\]<br \/>\n\uc774\ub77c\uace0 \uc815\uc758\ud558\uc790. \uc774\ub54c \uc801\ub2f9\ud55c \uc815\uc218 \\(n_0\\)\uc5d0 \ub300\ud558\uc5ec \\(Z_{n_0}\\)\ub97c \uc815\uc758\uc5ed\uc73c\ub85c \ud558\ub294 \ud568\uc218 \\(a\\)\ub97c <span class=\"defined\">\ubb34\ud55c\uc218\uc5f4<\/span>\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc5ec\uae30\uc11c \ud568\uc218 \\(a\\)\ub97c \\(\\left\\{a_n \\right\\}\\)\uc73c\ub85c \ub098\ud0c0\ub0b4\uba70, \uc815\uc218 \\(n\\)\uc5d0 \ub300\ud55c \ud568\uc218 \\(a\\)\uc758 \ud568\uc22b\uac12 \\(a(n)\\)\uc744 \\(a_n\\)\uc73c\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub610\ud55c \\(a_{n_0}\\)\ub97c \\(\\left\\{a_n\\right\\}\\)\uc758 <span class=\"defined\">\uccab\uc9f8\ud56d<\/span>(initial term) \ub610\ub294 <span class=\"defined\">\ucd08\ud56d<\/span>\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\uc218\uc5f4\uc758 \ubaa8\ub4e0 \ud56d\uc774 \\(\\mathbb{R}\\)\uc5d0 \uc18d\ud558\uba74, \uadf8 \uc218\uc5f4\uc744 <span class=\"defined\">\uc2e4\uc218\uc5f4<\/span>(real sequence)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc720\ub9ac\uc218\uc5f4(rational sequence), \ubcf5\uc18c\uc218\uc5f4(complex sequence), \ubca1\ud130\uc218\uc5f4(vector sequence)\ub3c4 \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uc815\uc758\ud55c\ub2e4.<\/p>\n<p>\uc218\uc5f4\uc758 \ud56d\uc774 \ud56d\uc0c1 \uc218(number)\uc778 \uac83\uc740 \uc544\ub2c8\uae30\uc5d0, \ucc45\uc5d0 \ub530\ub77c\uc11c\ub294 sequence\ub97c <span class=\"defined\">\uc810\uc5f4<\/span>\uc774\ub77c\uace0 \ubd80\ub974\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n<p>\ub9cc\uc57d \uc218\uc5f4 \\(\\left\\{a_n\\right\\}\\)\uc758 \uccab\uc9f8\ud56d\uc758 \ucca8\uc790 \\(n_0\\)\uac00 \uba85\ud655\ud558\uac8c \ub4dc\ub7ec\ub098\uc788\uc9c0 \uc54a\ub2e4\uba74, \uc74c\uc774 \uc544\ub2cc \uc815\uc218 \\(n_0\\) \uc911\uc5d0\uc11c [\\(n\\ge n_0\\)\uc778 \ubaa8\ub4e0 \\(n\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n\\)\uc774 \uc815\uc758]\ub418\ub294 \uac00\uc7a5 \uc791\uc740 \\(n_0\\)\ub97c \uccab\uc9f8\ud56d\uc758 \ucca8\uc790\ub85c \uc0bc\ub294\ub2e4. \uc608\ub97c \ub4e4\uc5b4,<br \/>\n\\[a_n = \\frac{1}{n(n-3)}\\]<br \/>\n\ub85c \uc8fc\uc5b4\uc9c4 \uc218\uc5f4 \\(\\left\\{a_n\\right\\}\\)\uc740 \\(a_4\\)\ub97c \uccab\uc9f8\ud56d\uc73c\ub85c \uc0bc\ub294\ub2e4.<\/p>\n<p>\uc218\uc5f4\uc758 \uadf9\ud55c\uc740 \ubb34\ud55c\uc218\uc5f4\uc5d0 \ub300\ud574\uc11c\ub9cc \uc815\uc758\ub418\ubbc0\ub85c, \uc774 \ucc45\uc5d0\uc11c \ubcc4\ub2e4\ub978 \uc5b8\uae09 \uc5c6\uc774 \uc218\uc5f4\uc774\ub77c \ud558\uba74 \ubb34\ud55c\uc218\uc5f4\uc744 \uc774\ub974\ub294 \uac83\uc73c\ub85c \uc57d\uc18d\ud55c\ub2e4.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<p><!--\n\n\n<h2 class=\"itc_h2\">\uc81c\ubaa9<\/h2>\n\n\n\n\n\n<p>.<\/p>\n\n\n\n\n\n<p>.<\/p>\n\n\n--><\/p>\n<p><!--\n\n\n\n<div class=\"theorem margintop2\">\n\n\n<p><span class=\"theorem\">\uc815\ub9ac 1.<\/span>\n\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<div class=\"proof\">\n\n\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n\n\n\n\n<p>\n\n<span class=\"qed\"><\/span><\/p>\n\n<\/div>\n\n\n\n\n########\n\n\n\n\n<div class=\"example\">\n\n\n<p><span class=\"example\">\ubcf4\uae30 1.<\/span>\n\n<\/p>\n\n<\/div>\n\n\n\n\n\n<h2 class=\"itc_h2\"><\/h2>\n\n\n\n--><\/p>\n<div style=\"display: none; visibility: hidden;\">\n\\[<br \/>\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}<br \/>\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}<br \/>\n\\newcommand{\\proj}{{\\operatorname{proj}}}<br \/>\n\\newcommand{\\adj}{{\\operatorname{adj}}}<br \/>\n\\]\n<\/div>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/euclidean-spaces\">\uc720\ud074\ub9ac\ub4dc \uacf5\uac04<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/limit-of-a-sequence\">\uc218\uc5f4\uc758 \uadf9\ud55c\uc758 \uc815\uc758<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 1\uc7a5 1\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \uc218\uc5f4(sequence)\uc774\ub780, \uc9c1\uad00\uc801\uc73c\ub85c \uc815\uc758\ud558\uc790\uba74, \\(a_1 ,\\, a_2 ,\\, a_3 ,\\, \\cdots\\) \uacfc \uac19\uc774 \uc218\ub97c \ud55c \uc904\ub85c \ub098\uc5f4\ud55c \uac83\uc774\ub2e4. \uc218\uc5f4\uc744 \uc774\ub8e8\uace0 \uc788\ub294 \uac01 \uc218\ub97c \ud56d(term)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \ud56d \\(a_n\\)\uc744 \\(\\boldsymbol{n}\\)\uc9f8 \ud56d\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \ud56d\uc758 \uc218\uac00 \uc720\ud55c\uc778 \uc218\uc5f4\uc744 \uc720\ud55c\uc218\uc5f4(finite sequence)\uc774\ub77c\uace0 \ubd80\ub974\uace0, \ud56d\uc758 \uc218\uac00 \ubb34\ud55c\uc778 \uc218\uc5f4\uc744 \ubb34\ud55c\uc218\uc5f4(infinite sequence)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc218\uc5f4 \\(a_1 ,\\, a_2 ,\\, a_3 ,\\, \\cdots\\) \uc744 \uac04\ub2e8\ud788&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":101,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"class_list":["post-6649","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6649","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=6649"}],"version-history":[{"count":40,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6649\/revisions"}],"predecessor-version":[{"id":7130,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6649\/revisions\/7130"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6620"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=6649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}