{"id":1570,"date":"2024-04-23T20:00:23","date_gmt":"2024-04-23T12:00:23","guid":{"rendered":"http:\/\/jiaohuweike.online\/?p=1570"},"modified":"2024-04-23T20:00:23","modified_gmt":"2024-04-23T12:00:23","slug":"liexiangs-2","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=1570","title":{"rendered":"\u6570\u5217\u6c42\u548c"},"content":{"rendered":"\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-711932c\" data-block-id=\"711932c\"><\/div>\n\n\n\n<div class=\"wp-block-stackable-heading stk-block-heading stk-block-heading--v2 stk-block stk-fa21366\" id=\"\u6570\u5217\u88c2\u9879\u6c42\u548c\" data-block-id=\"fa21366\"><h4 class=\"stk-block-heading__text\">\u6570\u5217\u88c2\u9879\u6c42\u548c<\/h4><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u6839\u636e\u6570\u5217\u7684\u901a\u9879\u516c\u5f0fa_n\uff0c\u6c42\u524dn\u9879\u548cS_n.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-1dda9ec\" data-block-id=\"1dda9ec\"><style>.stk-1dda9ec {height:30px !important;}<\/style><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.a_n=\\frac{1}{n(n+1)} ,\u6c42S_n\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848\uff1a<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n=\\frac{1}{n}-\\frac{1}{n+1} ,S_n=1-\\frac{1}{n+1}  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.a_n=\\frac{1}{n(n+2)} ,\u6c42S_n\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n=\\frac{1}{2}( \\frac{1}{n}-\\frac{1}{n+2}) ,S_n=\\frac{1}{2}( 1+\\frac{1}{2} -\\frac{1}{n+1} -\\frac{1}{n+2}  )~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.a_n=\\frac{4n^2}{(2n-1)(2n+1)} ,\u6c42S_n\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n= \\frac{4n^2-1+1}{4n^2-1} =1+\\frac{1}{(2n-1)(2n+1)}=1+\\frac{1}{2} (\\frac{1}{2n-1}-\\frac{1}{2n+1})~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\\therefore S_n=n+\\frac{1}{2}( 1-\\frac{1}{2n+1}  )~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.a_n=(-1)^n\\frac{4n}{(2n-1)(2n+1)} ,\u6c42S_n\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n=(-1)^n(\\frac{1}{2n-1}+\\frac{1}{2n+1} ),S_n=\\left\\{\\begin{matrix}\n \\displaystyle\\frac{-2n}{2n+1},n\u4e3a\u5076\u6570 &amp; \\\\\n \\displaystyle \\frac{-2n-2}{2n+1},n\u4e3a\u5947\u6570 &amp;\n\\end{matrix}\\right.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.a_n=\\frac{1}{n(n+1)(n+2)} ,\u6c42S_n\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n=\\frac{1}{2}[\\frac{1}{n(n+1)}-\\frac{1}{(n+1)(n+2)} ],S_n=\\frac{1}{2} [\\frac{1}{2}- \\frac{1}{(n+1)(n+2)} ]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>6.a_n=\\frac{2^n}{(2^n-1)(2^{n+1}-1)} ,\u6c42S_n\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n=\\frac{1}{2^n-1}-\\frac{1}{2^{n+1}-1} ,S_n=1-\\frac{1}{2^{n+1}-1}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>7.a_n=\\frac{n+2}{n(n+1)2^{n+1}} ,\u6c42S_n\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n=\\frac{1}{n2^n}-\\frac{1}{({n+1)2^{n+1}}} ,S_n=\\frac{1}{2} -\\frac{1}{({n+1)2^{n+1}}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>8.a_n=\\lg_{}{\\frac{n+1}{n} } ,\u6c42S_n.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n=\\lg_{}{(n+1)}-\\lg_{}{n}  ,S_n=\\lg_{}{(n+1)} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>9.a_n=\\frac{1}{\\sqrt{n+1}+\\sqrt{n}},\u6c42S_n.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_n=\\frac{1}{\\sqrt{n+1}+\\sqrt{n}}=\\frac{\\sqrt{n+1}-\\sqrt{n}}{1},S_n=\\sqrt{n+1}-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>10.a_1=1,\\frac{a_n}{a_{n-1}}=\\frac{n^2}{n^2-1},b_n=\\frac{a_n}{n^2},\u6c42\u6570\u5217\\{b_n\\}\u7684\u524dn\u9879\u548cS_n.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>S_n=\\frac{2n}{n+1};\u63d0\u793a\uff1a\\frac{a_n}{a_{n-1}}=\\frac{n^2}{n^2-1}=\\frac{n}{n-1}\\frac{n}{n+1},\u7d2f\u4e58\u5f97a_n==\\frac{2n}{n+1},S_n=\\frac{2n}{n+1}.~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\u5206\u7ec4\u3001\u516c\u5f0f\u6c42\u548c<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\u5728\u6570\u5217  \\left\\{a_{n}\\right\\}  \u4e2d\uff0c  a_{n}=\\left\\{\\begin{array}{l}2 n-1, n \\text { \u4e3a\u5947\u6570 } \\\\ \\left(-\\frac{\\sqrt{2}}{2}\\right)^{n-2}, n \\text { \u4e3a\u5076\u6570 }\\end{array}\\right. , \u524d  n  \u9879\u548c\u4e3a  S_{n}  \uff0c\u6c42 S_{2 n}.~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n \n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u7b54\u6848\uff1a2n^2-n+2-\\frac{1}{2^{n-1}};\u63d0\u793a\uff1aS_n=(a_1+a_3+\\dots)+(a_2+a_4+\\dots),\u5404n\u9879.~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n \n","protected":false},"excerpt":{"rendered":"<p>\u88c2\u9879\u6c42\u548c\uff0c\u5206\u7ec4\u6c42\u548c\uff0c\u516c\u5f0f<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[10],"tags":[37],"class_list":["post-1570","post","type-post","status-publish","format-standard","hentry","category-10","tag-37"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1570","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1570"}],"version-history":[{"count":0,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1570\/revisions"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1570"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}