{"id":6682,"date":"2021-07-20T23:54:02","date_gmt":"2021-07-20T14:54:02","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6682"},"modified":"2026-09-27T17:20:30","modified_gmt":"2026-09-27T08:20:30","slug":"infinite-series","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/infinite-series\/","title":{"rendered":"\ubb34\ud55c\uae09\uc218\uc758 \ub73b"},"content":{"rendered":"<div style=\"display: none; visibility: hidden;\">\n<style type=\"text\/css\">\n\timg.mfp-img { background-color: white; }\n<\/style>\n<p><!--\n\\[\n\\newcommand{\\vecf}{{\\mathbf{f}}}\n\\newcommand{\\vecL}{{\\mathbf{L}}}\n\\newcommand{\\vecR}{{\\mathbb{R}}}\n\\newcommand{\\imI}{\\boldsymbol{i}}\n\\]\n-->\n<\/div>\n<div class=\"box itc_intro\">\n<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 2\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><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ubb34\ud55c\uae09\uc218\uc758 \ub73b<\/h2>\n<p>\uc720\ud55c \uac1c\uc758 \uc218\ub97c \ub354\ud560 \ub54c\uc5d0\ub294 \ub367\uc148\uc744 \ubc18\ubcf5\ud558\uba74 \uadf8 \ud569\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4. \uadf8\ub7ec\ub098 \ubb34\ud55c\ud788 \ub9ce\uc740 \uc218\ub97c \ub354\ud558\ub294 \uac83\uc740 \uc720\ud55c\ud55c \ub367\uc148\ub9cc\uc73c\ub85c \uc815\uc758\ud560 \uc218 \uc5c6\ub2e4. \uc774\ub54c \uc55e \uc7a5\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \uc218\uc5f4\uc758 \uadf9\ud55c\uc744 \uc774\uc6a9\ud558\uc5ec \ubb34\ud55c\ud55c \ud569\uc758 \uc758\ubbf8\ub97c \uc815\uc758\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p>\uc774 \uc808\uc5d0\uc11c\ub294 \ud3b8\uc758\uc0c1 \\(a_1\\)\ubd80\ud130 \uc2dc\uc791\ud558\ub294 \uc2e4\uc218\uc5f4 \\(\\left\\{a_n\\right\\}\\)\uc744 \uc0dd\uac01\ud558\uc790. \uc218\uc5f4\uc758 \ud56d\uc744 \uc21c\uc11c\ub300\ub85c \ub367\uc148\uae30\ud638\ub85c \uc5f0\uacb0\ud55c \ud615\uc2dd\uc801\uc778 \uc2dd<br \/>\n\\[<br \/>\na_1+a_2+a_3+\\cdots<br \/>\n\\]<br \/>\n\uc744 \\(\\left\\{a_n\\right\\}\\)\uc758 <span class=\"defined\">\ubb34\ud55c\uae09\uc218<\/span>(infinite series), \ub610\ub294 \uac04\ub2e8\ud788 <span class=\"defined\">\uae09\uc218<\/span>(series)\ub77c\uace0 \ubd80\ub974\uace0<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n<br \/>\n\\]<br \/>\n\uacfc \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4. \uc774 \ub2e8\uacc4\uc5d0\uc11c \ubb34\ud55c\uae09\uc218\ub294 \uc544\uc9c1 \ud558\ub098\uc758 \uc2e4\uc22b\uac12\uc744 \ub73b\ud558\uc9c0 \uc54a\uace0 \ud615\uc2dd\uc801\uc778 \uc2dd\uc744 \ub73b\ud55c\ub2e4.<\/p>\n<p>\uc591\uc758 \uc815\uc218 \\(n\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\nS_n<br \/>\n=<br \/>\n\\sum_{k=1}^{n}a_k<br \/>\n=<br \/>\na_1+a_2+\\cdots+a_n<br \/>\n\\]<br \/>\n\uc774\ub77c\uace0 \ud558\uc790. \\(S_n\\)\uc744 \uae09\uc218\uc758 <span class=\"defined\">\\(\\boldsymbol{n}\\)\ubc88\uc9f8 \ubd80\ubd84\ud569<\/span>(partial sum)\uc774\ub77c\uace0 \ubd80\ub974\uace0, \uc218\uc5f4<br \/>\n\\[<br \/>\n\\left\\{S_n\\right\\}<br \/>\n\\]<br \/>\n\uc744 <span class=\"defined\">\ubd80\ubd84\ud569\uc218\uc5f4<\/span>(sequence of partial sums)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\ubd80\ubd84\ud569\uc218\uc5f4 \\(\\left\\{S_n\\right\\}\\)\uc774 \uc5b4\ub5a4 \uc2e4\uc218 \\(S\\)\uc5d0 \uc218\ub834\ud558\uba74 \ubb34\ud55c\uae09\uc218<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n<br \/>\n\\]<br \/>\n\uac00 <span class=\"defined\">\uc218\ub834<\/span>(converge)\ud55c\ub2e4\uace0 \ub9d0\ud558\uace0, \\(S\\)\ub97c \uc774 \uae09\uc218\uc758 <span class=\"defined\">\ud569<\/span>(sum)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc989<br \/>\n\\[<br \/>\n\\lim_{n\\rightarrow\\infty}S_n=S<br \/>\n\\]<br \/>\n\uc774\uba74<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n=S<br \/>\n\\]<br \/>\n\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\ubd80\ubd84\ud569\uc218\uc5f4\uc774 \uc5b4\ub5a0\ud55c \uc2e4\uc218\uc5d0\ub3c4 \uc218\ub834\ud558\uc9c0 \uc54a\uc73c\uba74 \ubb34\ud55c\uae09\uc218\uac00 <span class=\"defined\">\ubc1c\uc0b0<\/span>(diverge)\ud55c\ub2e4\uace0 \ub9d0\ud55c\ub2e4. \ud2b9\ud788<br \/>\n\\[<br \/>\nS_n\\rightarrow\\infty<br \/>\n\\]<br \/>\n\uc774\uba74<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n=\\infty<br \/>\n\\]<br \/>\n\ub77c\uace0 \uc4f0\uace0, \uae09\uc218\uac00 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4\uace0 \ub9d0\ud55c\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c<br \/>\n\\[<br \/>\nS_n\\rightarrow-\\infty<br \/>\n\\]<br \/>\n\uc774\uba74<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n=-\\infty<br \/>\n\\]<br \/>\n\ub77c\uace0 \uc4f4\ub2e4. \uc5ec\uae30\uc11c \\(\\infty\\)\uc640 \\(-\\infty\\)\ub294 \uae09\uc218\uc758 \uc2e4\uc22b\uac12\uc774 \uc544\ub2c8\ub77c \ubc1c\uc0b0\uc758 \uc591\uc0c1\uc744 \ub098\ud0c0\ub0b4\ub294 \uae30\ud638\uc774\ub2e4.<\/p>\n<p>\ub530\ub77c\uc11c \uae30\ud638<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n<br \/>\n\\]<br \/>\n\uc740 \ubb38\ub9e5\uc5d0 \ub530\ub77c \ubb34\ud55c\uae09\uc218\ub77c\ub294 \ud615\uc2dd\uc801\uc778 \uc2dd\uc744 \ub098\ud0c0\ub0b4\uae30\ub3c4 \ud558\uace0, \uae09\uc218\uac00 \uc218\ub834\ud560 \ub54c\uc5d0\ub294 \uadf8 \ud569\uc744 \ub098\ud0c0\ub0b4\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 2.1.1.<\/span><br \/>\n\ub2e4\uc74c \ubb34\ud55c\uae09\uc218\uc758 \uc218\ub834 \uc5ec\ubd80\ub97c \uc870\uc0ac\ud558\uace0, \uc218\ub834\ud558\ub294 \uacbd\uc6b0 \uadf8 \ud569\uc744 \uad6c\ud558\uc2dc\uc624.<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\frac{1}{(n+1)(n+2)}<br \/>\n\\]\n<\/p>\n<p><span class=\"proof\">\ud480\uc774.<\/span><br \/>\n\\[<br \/>\n\\frac{1}{(k+1)(k+2)}<br \/>\n=<br \/>\n\\frac{1}{k+1}-\\frac{1}{k+2}<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c \\(n\\)\ubc88\uc9f8 \ubd80\ubd84\ud569\uc740<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\nS_n<br \/>\n&#038;=<br \/>\n\\sum_{k=1}^{n}<br \/>\n\\frac{1}{(k+1)(k+2)}<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\left(\\frac12-\\frac13\\right)<br \/>\n+<br \/>\n\\left(\\frac13-\\frac14\\right)<br \/>\n+\\cdots+<br \/>\n\\left(\\frac{1}{n+1}-\\frac{1}{n+2}\\right)<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\frac12-\\frac{1}{n+2}.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c<br \/>\n\\[<br \/>\n\\lim_{n\\rightarrow\\infty}S_n<br \/>\n=<br \/>\n\\frac12.<br \/>\n\\]<br \/>\n\uadf8\ub7ec\ubbc0\ub85c \uc8fc\uc5b4\uc9c4 \ubb34\ud55c\uae09\uc218\ub294 \uc218\ub834\ud558\uba70 \uadf8 \ud569\uc740<br \/>\n\\[<br \/>\n\\frac12<br \/>\n\\]<br \/>\n\uc774\ub2e4.<\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 2.1.2.<\/span><br \/>\n\ub2e4\uc74c \ubb34\ud55c\uae09\uc218\uc758 \uc218\ub834 \uc5ec\ubd80\ub97c \uc870\uc0ac\ud558\uace0, \uc218\ub834\ud558\ub294 \uacbd\uc6b0 \uadf8 \ud569\uc744 \uad6c\ud558\uc2dc\uc624.<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\frac{1}{\\sqrt{n+1}+\\sqrt n}<br \/>\n\\]\n<\/p>\n<p><span class=\"proof\">\ud480\uc774.<\/span><br \/>\n\uc77c\ubc18\ud56d\uc744 \uc720\ub9ac\ud654\ud558\uba74<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\n\\frac{1}{\\sqrt{n+1}+\\sqrt n}<br \/>\n&#038;=<br \/>\n\\frac{\\sqrt{n+1}-\\sqrt n}<br \/>\n{(\\sqrt{n+1}+\\sqrt n)(\\sqrt{n+1}-\\sqrt n)}<br \/>\n\\\\<br \/>\n&#038;=<br \/>\n\\sqrt{n+1}-\\sqrt n.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\nS_n<br \/>\n&#038;=<br \/>\n\\sum_{k=1}^{n}<br \/>\n\\left(<br \/>\n\\sqrt{k+1}-\\sqrt k<br \/>\n\\right)<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n(\\sqrt2-\\sqrt1)<br \/>\n+<br \/>\n(\\sqrt3-\\sqrt2)<br \/>\n+\\cdots+<br \/>\n(\\sqrt{n+1}-\\sqrt n)<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\sqrt{n+1}-1.<br \/>\n\\end{aligned}<br \/>\n\\]<br \/>\n\uadf8\ub7ec\ubbc0\ub85c<br \/>\n\\[<br \/>\nS_n\\rightarrow\\infty.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c \uc8fc\uc5b4\uc9c4 \ubb34\ud55c\uae09\uc218\ub294 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4.<\/p>\n<\/div>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ubb34\ud55c\uae09\uc218\uc758 \uacc4\uc0b0<\/h2>\n<p>\ubb34\ud55c\uae09\uc218\uc758 \uc218\ub834\uacfc \ud569\uc740 \ubd80\ubd84\ud569\uc218\uc5f4\uc758 \uadf9\ud55c\uc73c\ub85c \uc815\uc758\ub41c\ub2e4. \ub530\ub77c\uc11c \uc218\uc5f4\uc758 \uadf9\ud55c\uc5d0 \uad00\ud55c \uc131\uc9c8\ub85c\ubd80\ud130 \ubb34\ud55c\uae09\uc218\uc758 \uae30\ubcf8 \uc131\uc9c8\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 2.1.1. (\ubb34\ud55c\uae09\uc218\uc758 \uc120\ud615\uc131)<\/span><\/p>\n<p>\ub450 \ubb34\ud55c\uae09\uc218<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n,<br \/>\n\\qquad<br \/>\n\\sum_{n=1}^{\\infty}b_n<br \/>\n\\]<br \/>\n\uc774 \ubaa8\ub450 \uc218\ub834\ud558\uace0 \uadf8 \ud569\uc774 \uac01\uac01 \\(S,T\\)\ub77c\uace0 \ud558\uc790. \\(k\\)\uac00 \uc2e4\uc218\uc774\uba74 \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n<ol class=\"bracket\">\n<li>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}ka_n=kS.<br \/>\n\\]\n<\/li>\n<li>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}(a_n+b_n)=S+T.<br \/>\n\\]\n<\/li>\n<li>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}(a_n-b_n)=S-T.<br \/>\n\\]\n<\/li>\n<\/ol>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\n\\[<br \/>\nA_n=\\sum_{j=1}^{n}a_j,<br \/>\n\\qquad<br \/>\nB_n=\\sum_{j=1}^{n}b_j<br \/>\n\\]<br \/>\n\ub77c\uace0 \ud558\uc790. \uac00\uc815\uc5d0 \uc758\ud558\uc5ec<br \/>\n\\[<br \/>\nA_n\\rightarrow S,<br \/>\n\\qquad<br \/>\nB_n\\rightarrow T.<br \/>\n\\]\n<\/p>\n<p>\uae09\uc218 \\(\\sum ka_n\\)\uc758 \\(n\\)\ubc88\uc9f8 \ubd80\ubd84\ud569\uc740<br \/>\n\\[<br \/>\n\\sum_{j=1}^{n}ka_j<br \/>\n=<br \/>\nkA_n<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\nkA_n\\rightarrow kS.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}ka_n=kS.<br \/>\n\\]\n<\/p>\n<p>\ub9c8\ucc2c\uac00\uc9c0\ub85c<br \/>\n\\[<br \/>\n\\sum_{j=1}^{n}(a_j+b_j)<br \/>\n=<br \/>\nA_n+B_n<br \/>\n\\rightarrow<br \/>\nS+T<br \/>\n\\]<br \/>\n\uc774\uace0<br \/>\n\\[<br \/>\n\\sum_{j=1}^{n}(a_j-b_j)<br \/>\n=<br \/>\nA_n-B_n<br \/>\n\\rightarrow<br \/>\nS-T.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c (2)\uc640 (3)\ub3c4 \uc131\ub9bd\ud55c\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 2.1.3.<\/span><br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n=3,<br \/>\n\\qquad<br \/>\n\\sum_{n=1}^{\\infty}b_n=-4<br \/>\n\\]<br \/>\n\uc77c \ub54c \ub2e4\uc74c \ubb34\ud55c\uae09\uc218\uc758 \ud569\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\displaystyle\\sum_{n=1}^{\\infty}(3a_n-b_n)\\)<\/li>\n<li>\\(\\displaystyle\\sum_{n=1}^{\\infty}(2a_n+5b_n)\\)<\/li>\n<\/ol>\n<p><span class=\"proof\">\ud480\uc774.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li>\n\\[<br \/>\n\\begin{aligned}<br \/>\n\\sum_{n=1}^{\\infty}(3a_n-b_n)<br \/>\n&#038;=<br \/>\n3\\sum_{n=1}^{\\infty}a_n<br \/>\n&#8211;<br \/>\n\\sum_{n=1}^{\\infty}b_n<br \/>\n\\\\<br \/>\n&#038;=<br \/>\n3\\cdot3-(-4)<br \/>\n=<br \/>\n13.<br \/>\n\\end{aligned}<br \/>\n\\]\n<\/li>\n<li>\n\\[<br \/>\n\\begin{aligned}<br \/>\n\\sum_{n=1}^{\\infty}(2a_n+5b_n)<br \/>\n&#038;=<br \/>\n2\\sum_{n=1}^{\\infty}a_n<br \/>\n+<br \/>\n5\\sum_{n=1}^{\\infty}b_n<br \/>\n\\\\<br \/>\n&#038;=<br \/>\n2\\cdot3+5(-4)<br \/>\n=<br \/>\n-14.<br \/>\n\\end{aligned}<br \/>\n\\]\n<\/li>\n<\/ol>\n<\/div>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 2.1.2. (\uc77c\ubc18\ud56d \ud310\uc815\ubc95)<\/span><\/p>\n<p>\ubb34\ud55c\uae09\uc218<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n<br \/>\n\\]<br \/>\n\uc774 \uc218\ub834\ud558\uba74<br \/>\n\\[<br \/>\na_n\\rightarrow0.<br \/>\n\\]<br \/>\n\ub530\ub77c\uc11c \\(a_n\\)\uc774 \\(0\\)\uc5d0 \uc218\ub834\ud558\uc9c0 \uc54a\uc73c\uba74 \ubb34\ud55c\uae09\uc218<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n<br \/>\n\\]<br \/>\n\uc740 \ubc1c\uc0b0\ud55c\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\\(n\\)\ubc88\uc9f8 \ubd80\ubd84\ud569\uc744<br \/>\n\\[<br \/>\nS_n=\\sum_{k=1}^{n}a_k<br \/>\n\\]<br \/>\n\ub77c\uace0 \ud558\uc790. \uae09\uc218\uac00 \uc218\ub834\ud558\uace0 \uadf8 \ud569\uc774 \\(S\\)\uc774\uba74<br \/>\n\\[<br \/>\nS_n\\rightarrow S.<br \/>\n\\]<br \/>\n\ub610\ud55c \ucca8\uc790\ub97c \ud558\ub098 \uc62e\uae34 \uc218\uc5f4\ub3c4 \uac19\uc740 \uac12\uc5d0 \uc218\ub834\ud558\ubbc0\ub85c<br \/>\n\\[<br \/>\nS_{n-1}\\rightarrow S.<br \/>\n\\]<br \/>\n\\(n\\ge2\\)\uc77c \ub54c<br \/>\n\\[<br \/>\na_n=S_n-S_{n-1}<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\n\\lim_{n\\rightarrow\\infty}a_n<br \/>\n=<br \/>\nS-S<br \/>\n=<br \/>\n0.<br \/>\n\\]<br \/>\n<span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 2.1.4.<\/span><br \/>\n\ubb34\ud55c\uae09\uc218<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}(-1)^n<br \/>\n\\]<br \/>\n\uc740 \ubc1c\uc0b0\ud55c\ub2e4. \uc2e4\uc81c\ub85c \uc77c\ubc18\ud56d \\((-1)^n\\)\uc740 \\(0\\)\uc5d0 \uc218\ub834\ud558\uc9c0 \uc54a\uc73c\ubbc0\ub85c \uc815\ub9ac 2.1.2\uc5d0 \uc758\ud558\uc5ec \uc774 \uae09\uc218\ub294 \uc218\ub834\ud560 \uc218 \uc5c6\ub2e4.<\/p>\n<\/div>\n<p><span class=\"remark\">\uc8fc\uc758.<\/span><br \/>\n\uc815\ub9ac 2.1.2\uc758 \uc5ed\uc740 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294\ub2e4. \uc989<br \/>\n\\[<br \/>\na_n\\rightarrow0<br \/>\n\\]<br \/>\n\uc774\ub77c\ub294 \uc0ac\uc2e4\ub9cc\uc73c\ub85c<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}a_n<br \/>\n\\]<br \/>\n\uc774 \uc218\ub834\ud55c\ub2e4\uace0 \uacb0\ub860 \ub0b4\ub9b4 \uc218 \uc5c6\ub2e4. \uc608\ub97c \ub4e4\uc5b4<br \/>\n\\[<br \/>\n\\frac{1}{\\sqrt{n+1}+\\sqrt n}<br \/>\n\\rightarrow0<br \/>\n\\]<br \/>\n\uc774\uc9c0\ub9cc \uc608\uc81c 2.1.2\uc5d0\uc11c \ubcf4\uc558\ub4ef\uc774<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\frac{1}{\\sqrt{n+1}+\\sqrt n}<br \/>\n\\]<br \/>\n\uc740 \uc591\uc758 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud55c\ub2e4.<\/p>\n<p><!-- ##################################################################### --><\/p>\n<h2 class=\"itc_h2\">\ubb34\ud55c\ub4f1\ube44\uae09\uc218<\/h2>\n<p>\ub4f1\ube44\uc218\uc5f4\uc758 \ud56d\ub4e4\uc744 \ucc28\ub840\ub85c \ub354\ud558\uc5ec \ub9cc\ub4e0 \ubb34\ud55c\uae09\uc218\ub97c <span class=\"defined\">\ubb34\ud55c\ub4f1\ube44\uae09\uc218<\/span>, <span class=\"defined\">\ub4f1\ube44\uae09\uc218<\/span> \ub610\ub294 <span class=\"defined\">\uae30\ud558\uae09\uc218<\/span>(geometric series)\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<p>\\(a\\ne0\\)\uc774\uace0 \\(r\\)\uac00 \uc2e4\uc218\ub77c\uace0 \ud558\uc790. \ub4f1\ube44\uc218\uc5f4<br \/>\n\\[<br \/>\na_n=ar^{n-1}<br \/>\n\\]<br \/>\n\uc5d0 \ub300\uc751\ud558\ub294 \ubb34\ud55c\ub4f1\ube44\uae09\uc218\ub294<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}ar^{n-1}<br \/>\n=<br \/>\na+ar+ar^2+\\cdots<br \/>\n\\]<br \/>\n\uc774\ub2e4.<\/p>\n<div class=\"theorem margintop2\">\n<p><span class=\"theorem\">\uc815\ub9ac 2.1.3. (\ubb34\ud55c\ub4f1\ube44\uae09\uc218\uc758 \ud569)<\/span><\/p>\n<p>\\(a\\ne0\\)\uc77c \ub54c \ubb34\ud55c\ub4f1\ube44\uae09\uc218<br \/>\n\\[<br \/>\n\\sum_{n=1}^{\\infty}ar^{n-1}<br \/>\n\\]<br \/>\n\uc774 \uc218\ub834\ud560 \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740<br \/>\n\\[<br \/>\n|r| < 1\n\\]\n\uc778 \uac83\uc774\ub2e4. \uc774\ub54c \uae09\uc218\uc758 \ud569\uc740\n\\[\n\\sum_{n=1}^{\\infty}ar^{n-1}\n=\n\\frac{a}{1-r}\n\\]\n\uc774\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85.<\/p>\n<p>\\(r\\ne1\\)\uc774\ub77c\uace0 \ud558\uc790. \\(n\\)\ubc88\uc9f8 \ubd80\ubd84\ud569\uc744 \\(S_n\\)\uc774\ub77c\uace0 \ud558\uba74<br \/>\n\\[<br \/>\nS_n<br \/>\n=<br \/>\na+ar+\\cdots+ar^{n-1}.<br \/>\n\\]<br \/>\n\uc591\ubcc0\uc5d0 \\(r\\)\ub97c \uacf1\ud558\uba74<br \/>\n\\[<br \/>\nrS_n<br \/>\n=<br \/>\nar+ar^2+\\cdots+ar^n.<br \/>\n\\]<br \/>\n\ub450 \uc2dd\uc744 \ube7c\uba74<br \/>\n\\[<br \/>\n(1-r)S_n<br \/>\n=<br \/>\na(1-r^n)<br \/>\n\\]<br \/>\n\uc774\ubbc0\ub85c<br \/>\n\\[<br \/>\nS_n<br \/>\n=<br \/>\n\\frac{a(1-r^n)}{1-r}.<br \/>\n\\]\n<\/p>\n<p>\ub9cc\uc57d<br \/>\n\\[<br \/>\n|r| < 1\n\\]\n\uc774\uba74 \uc815\ub9ac 1.4.1\uc5d0 \uc758\ud558\uc5ec\n\\[\nr^n\\rightarrow0.\n\\]\n\ub530\ub77c\uc11c\n\\[\nS_n\n\\rightarrow\n\\frac{a}{1-r}.\n\\]\n\uadf8\ub7ec\ubbc0\ub85c \uae09\uc218\ub294 \uc218\ub834\ud558\uace0 \uadf8 \ud569\uc740\n\\[\n\\frac{a}{1-r}\n\\]\n\uc774\ub2e4.<\/p>\n<p>\ubc18\ub300\ub85c<br \/>\n\\[<br \/>\n|r|\\ge1<br \/>\n\\]<br \/>\n\uc774\ub77c\uace0 \ud558\uc790. \\(a\\ne0\\)\uc774\ubbc0\ub85c \uc77c\ubc18\ud56d<br \/>\n\\[<br \/>\nar^{n-1}<br \/>\n\\]<br \/>\n\uc740 \\(0\\)\uc5d0 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4. \ub530\ub77c\uc11c \uc815\ub9ac 2.1.2\uc5d0 \uc758\ud558\uc5ec \uae09\uc218\ub294 \ubc1c\uc0b0\ud55c\ub2e4. \ud2b9\ud788 \\(r=1\\)\uc77c \ub54c\uc5d0\ub3c4 \uc77c\ubc18\ud56d\uc740 \ud56d\uc0c1 \\(a\\ne0\\)\uc774\ubbc0\ub85c \ubc1c\uc0b0\ud55c\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 2.1.5.<\/span><br \/>\n\ub2e4\uc74c \ubb34\ud55c\uae09\uc218\uc758 \uc218\ub834 \uc5ec\ubd80\ub97c \uc870\uc0ac\ud558\uace0, \uc218\ub834\ud558\ub294 \uacbd\uc6b0 \uadf8 \ud569\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\n\\[<br \/>\n1+\\frac23+\\left(\\frac23\\right)^2+\\left(\\frac23\\right)^3+\\cdots<br \/>\n\\]\n<\/li>\n<li>\n\\[<br \/>\n1-\\frac43+\\left(\\frac43\\right)^2-\\left(\\frac43\\right)^3+\\cdots<br \/>\n\\]\n<\/li>\n<\/ol>\n<p><span class=\"proof\">\ud480\uc774.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li>\uacf5\ube44\uac00 \\(\\frac23\\)\uc778 \ubb34\ud55c\ub4f1\ube44\uae09\uc218\uc774\ub2e4. \uacf5\ube44\uc758 \uc808\ub313\uac12\uc774 \\(1\\)\ubcf4\ub2e4 \uc791\uc73c\ubbc0\ub85c \uc218\ub834\ud558\uba70 \uadf8 \ud569\uc740<br \/>\n\\[<br \/>\n\\frac{1}{1-\\frac23}<br \/>\n=<br \/>\n3<br \/>\n\\]<br \/>\n\uc774\ub2e4.<\/li>\n<li>\uacf5\ube44\uac00 \\(-\\frac43\\)\uc778 \ubb34\ud55c\ub4f1\ube44\uae09\uc218\uc774\ub2e4. \uacf5\ube44\uc758 \uc808\ub313\uac12\uc774 \\(1\\)\ubcf4\ub2e4 \ud06c\ubbc0\ub85c \ubc1c\uc0b0\ud55c\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 2.1.6.<\/span><br \/>\n\ub2e4\uc74c \ubb34\ud55c\uae09\uc218\uc758 \ud569\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(\\displaystyle\\sum_{n=1}^{\\infty}\\frac{3^n+4^n}{5^n}\\)<\/li>\n<li>\\(\\displaystyle\\sum_{n=1}^{\\infty}\\frac{(-2)^n+5^n}{(-6)^n}\\)<\/li>\n<\/ol>\n<p><span class=\"proof\">\ud480\uc774.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li>\n\\[<br \/>\n\\begin{aligned}<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\frac{3^n+4^n}{5^n}<br \/>\n&#038;=<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\left(\\frac35\\right)^n<br \/>\n+<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\left(\\frac45\\right)^n<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\frac{\\frac35}{1-\\frac35}<br \/>\n+<br \/>\n\\frac{\\frac45}{1-\\frac45}<br \/>\n\\\\<br \/>\n&#038;=<br \/>\n\\frac32+4<br \/>\n=<br \/>\n\\frac{11}{2}.<br \/>\n\\end{aligned}<br \/>\n\\]\n<\/li>\n<li>\n\\[<br \/>\n\\begin{aligned}<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\frac{(-2)^n+5^n}{(-6)^n}<br \/>\n&#038;=<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\left(\\frac13\\right)^n<br \/>\n+<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n\\left(-\\frac56\\right)^n<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\frac{\\frac13}{1-\\frac13}<br \/>\n+<br \/>\n\\frac{-\\frac56}{1+\\frac56}<br \/>\n\\\\<br \/>\n&#038;=<br \/>\n\\frac12-\\frac5{11}<br \/>\n=<br \/>\n\\frac1{22}.<br \/>\n\\end{aligned}<br \/>\n\\]\n<\/li>\n<\/ol>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 2.1.7.<\/span><br \/>\n\ubb34\ud55c\ub4f1\ube44\uae09\uc218\uc758 \ud569\uc744 \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c \uc21c\ud658\uc18c\uc218\ub97c \ubd84\uc218\ub85c \ub098\ud0c0\ub0b4\uc2dc\uc624.<\/p>\n<ol class=\"parenthesis\">\n<li>\\(0.0\\dot{1}\\dot{2}\\)<\/li>\n<li>\\(1.\\dot{0}1\\dot{2}\\)<\/li>\n<\/ol>\n<p><span class=\"proof\">\ud480\uc774.<\/span><\/p>\n<ol class=\"parenthesis\">\n<li>\n\\[<br \/>\n\\begin{aligned}<br \/>\n0.0\\dot{1}\\dot{2}<br \/>\n&#038;=<br \/>\n\\frac{12}{10^3}<br \/>\n+<br \/>\n\\frac{12}{10^5}<br \/>\n+<br \/>\n\\frac{12}{10^7}<br \/>\n+\\cdots<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\frac{12}{10^3}<br \/>\n\\left(<br \/>\n1+\\frac1{100}+\\frac1{100^2}+\\cdots<br \/>\n\\right)<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n\\frac{12}{1000}<br \/>\n\\cdot<br \/>\n\\frac{1}{1-\\frac1{100}}<br \/>\n\\\\<br \/>\n&#038;=<br \/>\n\\frac{2}{165}.<br \/>\n\\end{aligned}<br \/>\n\\]\n<\/li>\n<li>\n\\[<br \/>\n\\begin{aligned}<br \/>\n1.\\dot{0}1\\dot{2}<br \/>\n&#038;=<br \/>\n1<br \/>\n+<br \/>\n\\frac{12}{1000}<br \/>\n+<br \/>\n\\frac{12}{1000^2}<br \/>\n+<br \/>\n\\frac{12}{1000^3}<br \/>\n+\\cdots<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n1<br \/>\n+<br \/>\n\\frac{12}{1000}<br \/>\n\\left(<br \/>\n1+\\frac1{1000}+\\frac1{1000^2}+\\cdots<br \/>\n\\right)<br \/>\n\\\\[5pt]<br \/>\n&#038;=<br \/>\n1<br \/>\n+<br \/>\n\\frac{12}{1000}<br \/>\n\\cdot<br \/>\n\\frac{1}{1-\\frac1{1000}}<br \/>\n\\\\<br \/>\n&#038;=<br \/>\n1+\\frac{12}{999}<br \/>\n=<br \/>\n\\frac{337}{333}.<br \/>\n\\end{aligned}<br \/>\n\\]\n<\/li>\n<\/ol>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 2.1.8.<\/span><br \/>\n\uadf8\ub9bc\uacfc \uac19\uc774 \ud55c \ubcc0\uc758 \uae38\uc774\uac00 \\(4\\)\uc778 \uc815\uc0ac\uac01\ud615\uc744 \ud06c\uae30\uac00 \uac19\uc740 \\(4\\)\uac1c\uc758 \uc815\uc0ac\uac01\ud615\uc73c\ub85c \ub098\ub208 \ub4a4 \uadf8\uc911 \ud55c \uc870\uac01\uc5d0 \uc0c9\uc744 \uce60\ud55c\ub2e4. \uc0c9\uc774 \uce60\ud574\uc9c0\uc9c0 \uc54a\uc740 \\(3\\)\uac1c\uc758 \uc815\uc0ac\uac01\ud615 \uc870\uac01 \uc911 \ud558\ub098\ub97c \ud0dd\ud558\uc5ec \ub2e4\uc2dc \ud06c\uae30\uac00 \uac19\uc740 \\(4\\)\uac1c\uc758 \uc815\uc0ac\uac01\ud615\uc73c\ub85c \ub098\ub208 \ub4a4 \uadf8\uc911 \ud55c \uc870\uac01\uc5d0 \uc0c9\uc744 \uce60\ud55c\ub2e4. \uc774 \uacfc\uc815\uc744 \ubb34\ud55c\ud788 \ubc18\ubcf5\ud560 \ub54c \uc0c9\uce60\ub41c \uc815\uc0ac\uac01\ud615\ub4e4\uc758 \ub113\uc774\uc758 \ud569\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n<div style=\"margin-bottom: 2em;\"><img decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_01.png\" alt=\"\" width=\"172\" height=\"172\" class=\"aligncenter size-full wp-image-6956\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_01.png 687w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_01-300x300.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_01-150x150.png 150w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_01-585x585.png 585w\" sizes=\"(max-width: 172px) 100vw, 172px\" \/><\/div>\n<p><span class=\"proof\">\ud480\uc774.<\/span><br \/>\n\uadf8\ub9bc\uacfc \uac19\uc774 \ucc28\ub840\ub85c \uc0c9\uce60\ub418\ub294 \uc815\uc0ac\uac01\ud615\uc758 \ub113\uc774\ub97c<br \/>\n\\[<br \/>\nS_1,S_2,S_3,\\ldots<br \/>\n\\]<br \/>\n\ub77c\uace0 \ud558\uc790.<\/p>\n<div><img decoding=\"async\" src=\"\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_02.png\" alt=\"\" width=\"153\" height=\"153\" class=\"aligncenter size-full wp-image-6957\" srcset=\"https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_02.png 612w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_02-300x300.png 300w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_02-150x150.png 150w, https:\/\/sasamath.com\/blog\/wp-content\/uploads\/2021\/07\/ex_02_01_08_square_02-585x585.png 585w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><\/div>\n<p>\uadf8\ub7ec\uba74<br \/>\n\\[<br \/>\nS_1=4<br \/>\n\\]<br \/>\n\uc774\uace0, \ub9e4 \ub2e8\uacc4\uc5d0\uc11c \ud55c \ubcc0\uc758 \uae38\uc774\uac00 \uc808\ubc18\uc774 \ub418\ubbc0\ub85c \ub113\uc774\ub294 \uc55e \ub2e8\uacc4\uc758 \\(\\frac14\\)\ubc30\uac00 \ub41c\ub2e4. \ub530\ub77c\uc11c<br \/>\n\\[<br \/>\nS_n<br \/>\n=<br \/>\n4\\left(\\frac14\\right)^{n-1}.<br \/>\n\\]<br \/>\n\uadf8\ub7ec\ubbc0\ub85c \uc0c9\uce60\ub41c \uc815\uc0ac\uac01\ud615\ub4e4\uc758 \ub113\uc774\uc758 \ud569\uc740<br \/>\n\\[<br \/>\n\\begin{aligned}<br \/>\n\\sum_{n=1}^{\\infty}S_n<br \/>\n&#038;=<br \/>\n\\sum_{n=1}^{\\infty}<br \/>\n4\\left(\\frac14\\right)^{n-1}<br \/>\n\\\\<br \/>\n&#038;=<br \/>\n\\frac{4}{1-\\frac14}<br \/>\n=<br \/>\n\\frac{16}{3}.<br \/>\n\\end{aligned}<br \/>\n\\]\n<\/p>\n<\/div>\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\u201c\u201d\n\u2018\u2019\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<p><!--\n\n\n<div style=\"display: none; visibility: hidden;\">\n\\[\n\\newcommand{\\Hom}{{\\operatorname{Hom}}}\n\\newcommand{\\Mat}{{\\operatorname{Mat}}}\n\\newcommand{\\proj}{{\\operatorname{proj}}}\n\\newcommand{\\adj}{{\\operatorname{adj}}}\n\\]\n<\/div>\n\n\n--><\/p>\n<div class=\"box itc_prev_next_box\">\n<ul class=\"itc_ul\">\n<li class=\"itc_li_prev\">\uc55e\uc758 \uae00 : <a href=\"..\/limit-of-a-vector-sequence\">\ubca1\ud130\uc218\uc5f4\uc758 \uadf9\ud55c<\/a><\/li>\n<li class=\"itc_li_next\">\ub2e4\uc74c \uae00 : <a href=\"..\/series-of-nonnegative-terms\">\uc591\ud56d\uae09\uc218<\/a><\/li>\n<\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 2\uc7a5 1\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.&nbsp; (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30) \ubb34\ud55c\uae09\uc218\uc758 \ub73b \uc720\ud55c \uac1c\uc758 \uc218\ub97c \ub354\ud560 \ub54c\uc5d0\ub294 \ub367\uc148\uc744 \ubc18\ubcf5\ud558\uba74 \uadf8 \ud569\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4. \uadf8\ub7ec\ub098 \ubb34\ud55c\ud788 \ub9ce\uc740 \uc218\ub97c \ub354\ud558\ub294 \uac83\uc740 \uc720\ud55c\ud55c \ub367\uc148\ub9cc\uc73c\ub85c \uc815\uc758\ud560 \uc218 \uc5c6\ub2e4. \uc774\ub54c \uc55e \uc7a5\uc5d0\uc11c \uc0b4\ud3b4\ubcf8 \uc218\uc5f4\uc758 \uadf9\ud55c\uc744 \uc774\uc6a9\ud558\uc5ec \ubb34\ud55c\ud55c \ud569\uc758 \uc758\ubbf8\ub97c \uc815\uc758\ud560 \uc218 \uc788\ub2e4. \uc774 \uc808\uc5d0\uc11c\ub294 \ud3b8\uc758\uc0c1 \\(a_1\\)\ubd80\ud130 \uc2dc\uc791\ud558\ub294 \uc2e4\uc218\uc5f4 \\(\\left\\{a_n\\right\\}\\)\uc744 \uc0dd\uac01\ud558\uc790. \uc218\uc5f4\uc758 \ud56d\uc744 \uc21c\uc11c\ub300\ub85c \ub367\uc148\uae30\ud638\ub85c \uc5f0\uacb0\ud55c \ud615\uc2dd\uc801\uc778 \uc2dd&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":6620,"menu_order":201,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-6682","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6682","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=6682"}],"version-history":[{"count":31,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6682\/revisions"}],"predecessor-version":[{"id":10138,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/6682\/revisions\/10138"}],"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=6682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}