{"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":"2026-09-27T17:06:00","modified_gmt":"2026-09-27T08:06:00","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>\ubbf8\uc801\ubd84\ud559\uc5d0\uc11c \uadf9\ud55c\uc758 \uac1c\ub150\uc744 \uc774\ud574\ud558\uae30 \uc704\ud558\uc5ec \uba3c\uc800 \uc218\uc5f4\uc744 \uc0b4\ud3b4\ubcf4\uc790. \uc9c1\uad00\uc801\uc73c\ub85c <span class=\"defined\">\uc218\uc5f4<\/span>(sequence)\uc774\ub780<br \/>\n\\[<br \/>\na_1,\\,a_2,\\,a_3,\\,\\cdots<br \/>\n\\]<br \/>\n\uc640 \uac19\uc774 \ub300\uc0c1\uc744 \uc77c\uc815\ud55c \uc21c\uc11c\ub85c \ub098\uc5f4\ud55c \uac83\uc774\ub2e4. \uc218\uc5f4\uc744 \uc774\ub8e8\ub294 \uac01 \ub300\uc0c1\uc744 <span class=\"defined\">\ud56d<\/span>(term)\uc774\ub77c\uace0 \ubd80\ub974\uba70, \\(a_n\\)\uc744 <span class=\"defined\">\\(\\boldsymbol{n}\\)\uc9f8 \ud56d<\/span>\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc218\uc5f4\uc758 \uc815\uc758<\/h2>\n<p>\uc218\uc5f4\uc740 \ud568\uc218\uc758 \uac1c\ub150\uc744 \uc774\uc6a9\ud558\uc5ec \uc5c4\ubc00\ud558\uac8c \uc815\uc758\ud560 \uc218 \uc788\ub2e4. \\(n_0\\)\uac00 \uc815\uc218\uc77c \ub54c<br \/>\n\\[<br \/>\nZ_{n_0}<br \/>\n=<br \/>\n\\left\\{<br \/>\nn\\in\\mathbb{Z}<br \/>\n\\,\\middle|\\,<br \/>\nn\\ge n_0<br \/>\n\\right\\}<br \/>\n\\]<br \/>\n\ub77c\uace0 \ud558\uc790. \uc5b4\ub5a4 \uc9d1\ud569 \\(S\\)\uc5d0 \ub300\ud558\uc5ec \ud568\uc218<br \/>\n\\[<br \/>\na:Z_{n_0}\\rightarrow S<br \/>\n\\]<br \/>\n\ub97c \\(S\\)\uc758 \uc6d0\uc18c\ub97c \ud56d\uc73c\ub85c \uac16\ub294 <span class=\"defined\">\ubb34\ud55c\uc218\uc5f4<\/span>(infinite sequence)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\uc815\uc218 \\(n\\ge n_0\\)\uc5d0 \ub300\ud558\uc5ec \ud568\uc218 \\(a\\)\uc758 \ud568\uc22b\uac12 \\(a(n)\\)\uc744 \\(a_n\\)\uc73c\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub530\ub77c\uc11c \uc218\uc5f4 \\(a\\)\ub97c<br \/>\n\\[<br \/>\n(a_n)_{n=n_0}^{\\infty}<br \/>\n\\quad\\text{\ub610\ub294}\\quad<br \/>\n\\{a_n\\}_{n=n_0}^{\\infty}<br \/>\n\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4. \uccab\uc9f8\ud56d \\(a_{n_0}\\)\ub97c <span class=\"defined\">\ucd08\ud56d<\/span>(initial term)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uccab\uc9f8\ud56d\uc758 \ucca8\uc790\uac00 \ubb38\ub9e5\uc5d0\uc11c \ubd84\uba85\ud558\uba74 \uc218\uc5f4\uc744 \uac04\ub2e8\ud788<br \/>\n\\[<br \/>\n(a_n)<br \/>\n\\quad\\text{\ub610\ub294}\\quad<br \/>\n\\{a_n\\}<br \/>\n\\]<br \/>\n\uacfc \uac19\uc774 \ub098\ud0c0\ub0b4\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n<p>\uc5ec\uae30\uc11c \\(\\{a_n\\}\\)\uc740 \uc218\uc5f4\uc744 \ub098\ud0c0\ub0b4\uae30 \uc704\ud55c \uad00\uc2b5\uc801\uc778 \ud45c\uae30\uc774\uba70, \uc218\uc5f4\uc758 \ud56d\ub4e4\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc9d1\ud569\uc744 \ub73b\ud558\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. \uc218\uc5f4\uc5d0\uc11c\ub294 \ud56d\uc758 \uc21c\uc11c\uc640 \uac19\uc740 \uac12\uc774 \uba87 \ubc88 \ub098\ud0c0\ub098\ub294\uc9c0\uac00 \uc911\uc694\ud558\ub2e4. \uc608\ub97c \ub4e4\uc5b4<br \/>\n\\[<br \/>\n(1,\\,2,\\,1,\\,2,\\,\\ldots)<br \/>\n\\]<br \/>\n\uc640<br \/>\n\\[<br \/>\n(1,\\,1,\\,2,\\,2,\\,\\ldots)<br \/>\n\\]<br \/>\n\ub294 \uc11c\ub85c \ub2e4\ub978 \uc218\uc5f4\uc774\ub2e4.<\/p>\n<p>\ub610\ud55c \\(n_0\\le n_1\\)\uc778 \ub450 \uc815\uc218 \\(n_0,n_1\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\n\\left\\{<br \/>\nn\\in\\mathbb{Z}<br \/>\n\\,\\middle|\\,<br \/>\nn_0\\le n\\le n_1<br \/>\n\\right\\}<br \/>\n\\]<br \/>\n\ub97c \uc815\uc758\uc5ed\uc73c\ub85c \ud558\ub294 \ud568\uc218\ub97c <span class=\"defined\">\uc720\ud55c\uc218\uc5f4<\/span>(finite sequence)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc774 \uacbd\uc6b0 \uc218\uc5f4\uc740<br \/>\n\\[<br \/>\na_{n_0},\\,a_{n_0+1},\\,\\ldots,\\,a_{n_1}<br \/>\n\\]<br \/>\n\uacfc \uac19\uc774 \uc720\ud55c \uac1c\uc758 \ud56d\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uc5ec\ub7ec \uc885\ub958\uc758 \uc218\uc5f4<\/h2>\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. \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \ubaa8\ub4e0 \ud56d\uc774 \\(\\mathbb{Q}\\)\uc5d0 \uc18d\ud558\uba74 \uc720\ub9ac\uc218\uc5f4(rational sequence), \ubaa8\ub4e0 \ud56d\uc774 \\(\\mathbb{C}\\)\uc5d0 \uc18d\ud558\uba74 \ubcf5\uc18c\uc218\uc5f4(complex sequence)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \ub610\ud55c \ubaa8\ub4e0 \ud56d\uc774 \\(\\mathbb{R}^d\\)\uc5d0 \uc18d\ud558\uba74 \ubca1\ud130\uc218\uc5f4(vector sequence)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\ub354 \uc77c\ubc18\uc801\uc73c\ub85c \uc218\uc5f4\uc758 \ud56d\uc740 \ubc18\ub4dc\uc2dc \uc218\uc77c \ud544\uc694\uac00 \uc5c6\ub2e4. \uc5b4\ub5a4 \uc9d1\ud569 \\(S\\)\ub97c \ud0dd\ud558\ub354\ub77c\ub3c4 \\(S\\)\uc5d0 \uac12\uc744 \uac16\ub294 \uc218\uc5f4\uc744 \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \ud2b9\ud788 \uacf5\uac04\uc758 \uc810\ub4e4\uc744 \ud56d\uc73c\ub85c \uac16\ub294 \uc218\uc5f4\uc744 \ubb38\ud5cc\uc5d0 \ub530\ub77c <span class=\"defined\">\uc810\uc5f4<\/span>\uc774\ub77c\uace0 \ubd80\ub974\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\uccab\uc9f8\ud56d\uc758 \ucca8\uc790<\/h2>\n<p>\uc218\uc5f4\uc774 \uc2dd \\(a_n\\)\uc73c\ub85c \uc8fc\uc5b4\uc84c\uc9c0\ub9cc \uccab\uc9f8\ud56d\uc758 \ucca8\uc790\uac00 \uba85\uc2dc\ub418\uc5b4 \uc788\uc9c0 \uc54a\uc744 \ub54c\uc5d0\ub294 \ub2e4\uc74c \uad00\ub840\ub97c \uc0ac\uc6a9\ud55c\ub2e4. \uc74c\uc774 \uc544\ub2cc \uc815\uc218 \\(n_0\\) \uc911\uc5d0\uc11c \ubaa8\ub4e0 \uc815\uc218 \\(n\\ge n_0\\)\uc5d0 \ub300\ud558\uc5ec \\(a_n\\)\uc774 \uc815\uc758\ub418\ub3c4\ub85d \ud558\ub294 \uac00\uc7a5 \uc791\uc740 \\(n_0\\)\uac00 \uc874\uc7ac\ud558\uba74, \uadf8 \\(n_0\\)\ub97c \uccab\uc9f8\ud56d\uc758 \ucca8\uc790\ub85c \uc0bc\ub294\ub2e4.<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4<br \/>\n\\[<br \/>\na_n<br \/>\n=<br \/>\n\\frac{1}{n(n-3)}<br \/>\n\\]<br \/>\n\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc218\uc5f4\uc744 \uc0dd\uac01\ud558\uc790. \\(a_3\\)\uc740 \uc815\uc758\ub418\uc9c0 \uc54a\uc9c0\ub9cc \ubaa8\ub4e0 \uc815\uc218 \\(n\\ge4\\)\uc5d0 \ub300\ud574\uc11c\ub294 \\(a_n\\)\uc774 \uc815\uc758\ub41c\ub2e4. \ub530\ub77c\uc11c \uccab\uc9f8\ud56d\uc744<br \/>\n\\[<br \/>\na_4<br \/>\n\\]<br \/>\n\ub85c \uc0bc\ub294\ub2e4.<\/p>\n<p>\uccab\uc9f8\ud56d\uc758 \ucca8\uc790\uac00 \uba85\uc2dc\ub418\uc5b4 \uc788\ub2e4\uba74 \uba85\uc2dc\ub41c \ucca8\uc790\ub97c \uc6b0\uc120\ud55c\ub2e4. \ub610\ud55c \uc704 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \\(n_0\\)\uac00 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294 \uacbd\uc6b0\uc5d0\ub294 \uccab\uc9f8\ud56d\uc758 \ucca8\uc790\ub97c \ub530\ub85c \uc9c0\uc815\ud574\uc57c \ud55c\ub2e4.<\/p>\n<p>\uc218\uc5f4\uc758 \uadf9\ud55c\uc740 \ubb34\ud55c\uc218\uc5f4\uc5d0 \ub300\ud558\uc5ec \uc815\uc758\ud558\ubbc0\ub85c, \uc774 \ucc45\uc5d0\uc11c \ubcc4\ub2e4\ub978 \uc5b8\uae09 \uc5c6\uc774 \uc218\uc5f4\uc774\ub77c\uace0 \ud558\uba74 \ubb34\ud55c\uc218\uc5f4\uc744 \ub73b\ud558\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) \ubbf8\uc801\ubd84\ud559\uc5d0\uc11c \uadf9\ud55c\uc758 \uac1c\ub150\uc744 \uc774\ud574\ud558\uae30 \uc704\ud558\uc5ec \uba3c\uc800 \uc218\uc5f4\uc744 \uc0b4\ud3b4\ubcf4\uc790. \uc9c1\uad00\uc801\uc73c\ub85c \uc218\uc5f4(sequence)\uc774\ub780 \\( a_1,\\,a_2,\\,a_3,\\,\\cdots \\) \uc640 \uac19\uc774 \ub300\uc0c1\uc744 \uc77c\uc815\ud55c \uc21c\uc11c\ub85c \ub098\uc5f4\ud55c \uac83\uc774\ub2e4. \uc218\uc5f4\uc744 \uc774\ub8e8\ub294 \uac01 \ub300\uc0c1\uc744 \ud56d(term)\uc774\ub77c\uace0 \ubd80\ub974\uba70, \\(a_n\\)\uc744 \\(\\boldsymbol{n}\\)\uc9f8 \ud56d\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc218\uc5f4\uc758 \uc815\uc758 \uc218\uc5f4\uc740 \ud568\uc218\uc758 \uac1c\ub150\uc744 \uc774\uc6a9\ud558\uc5ec \uc5c4\ubc00\ud558\uac8c \uc815\uc758\ud560 \uc218 \uc788\ub2e4. \\(n_0\\)\uac00 \uc815\uc218\uc77c \ub54c \\( Z_{n_0} = \\left\\{ n\\in\\mathbb{Z} \\,\\middle|\\, n\\ge n_0 \\right\\} \\)&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":"no","_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":41,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6649\/revisions"}],"predecessor-version":[{"id":10131,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6649\/revisions\/10131"}],"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}]}}