{"id":1800,"date":"2024-06-03T18:09:20","date_gmt":"2024-06-03T10:09:20","guid":{"rendered":"http:\/\/www.jiaohuweike.online\/?p=1800"},"modified":"2025-11-09T11:04:07","modified_gmt":"2025-11-09T03:04:07","slug":"hsyldwt-2-3-2","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=1800","title":{"rendered":"\u6570\u5217\u7ecf\u5178\u9898\u76ee"},"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=\"\u9898\u76ee\" data-block-id=\"fa21366\"><h4 class=\"stk-block-heading__text\">\u9898\u76ee<\/h4><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(2021 \u5168\u56fd\u4e59\u5377)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u8bb0  S_{n}  \u4e3a\u6570\u5217  \\left\\{a_{n}\\right\\}  \u7684\u524d  n  \u9879\u548c,  b_{n}  \u4e3a\u6570\u5217  \\left\\{S_{n}\\right\\}  \u7684\u524d  n  \u9879\u79ef,\u5df2\u77e5  \\frac{2}{S_{n}}+\\frac{1}{b_{n}}=2 .~~~~~~~~~~~~~~~~~~~~~~\\\\\n(1)\u8bc1\u660e: \u6570\u5217  \\left\\{b_{n}\\right\\}  \u662f\u7b49\u5dee\u6570\u5217;\n(2)\u6c42  \\left\\{a_{n}\\right\\}  \u7684\u901a\u9879\u516c\u5f0f.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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>(1)  \\left\\{b_{n}\\right\\}  \u662f\u4ee5  \\frac{3}{2}  \u4e3a\u9996\u9879\uff0c  \\frac{1}{2}  \u4e3a\u516c\u5dee\u7684\u7b49\u5dee\u6570\u5217.\n(2)  a_{n}=\\left\\{\\begin{array}{l}\\frac{3}{2}, n=1, \\\\ -\\frac{1}{n(n+1)}, n \\geqslant 2 .\\end{array}\\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>(2023\u65b0\u9ad8\u8003 1 \u5377) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u8bbe\u7b49\u5dee\u6570\u5217  \\left\\{a_{n}\\right\\}  \u7684\u516c\u5dee\u4e3a  d , \u4e14  d&gt;1 . \u4ee4  b_{n}=\\frac{n^{2}+n}{a_{n}} , \u8bb0  S_{n}, T_{n}  \u5206\u522b\u4e3a\u6570\u5217  \\left\\{a_{n}\\right\\},\\left\\{b_{n}\\right\\}  \u7684\\\\\u524d  n  \u9879\u548c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(1)\u82e5  3 a_{2}=3 a_{1}+a_{3}, S_{3}+T_{3}=21 , \u6c42  \\left\\{a_{n}\\right\\}  \u7684\u901a\u9879\u516c\u5f0f;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(2)\u82e5  \\left\\{b_{n}\\right\\}  \u4e3a\u7b49\u5dee\u6570\u5217, \u4e14  S_{99}-T_{99}=99 , \u6c42  d .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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>(1)  a_{n}=3 n\uff1b(2) d=\\frac{51}{50} .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n<\/details>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u56fe\u4e2d\u7684\u6570\u9635\u6ee1\u8db3: \u6bcf\u4e00\u884c\u4ece\u5de6\u5230\u53f3\u6210\u7b49\u5dee\u6570\u5217, \u6bcf\u4e00\u5217\u4ece\u4e0a\u5230\u4e0b\u6210\u7b49\u6bd4\u6570\u5217, \u4e14~~~~~~~~~~\\\\\u516c\u6bd4\u5747\u4e3a\u5b9e\u6570  q, ~~a_{1,1}&gt;0, a_{1,3}=5, a_{2,2}=-6,a_{4,2}^{2}=a_{7,5}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n\\begin{matrix}\n  &amp;a_{1,1}  &amp;a_{1,2}  &amp;a_{1,3}  &amp;\\cdots   &amp;a_{1,n}&amp;\\cdots\\\\\n  &amp;a_{2,1}  &amp;a_{2,2}  &amp;a_{2,3}  &amp;\\cdots   &amp;a_{2,n}&amp;\\cdots\\\\\n  &amp;a_{3,1}  &amp;a_{3,2}  &amp;a_{3,3}  &amp;\\cdots   &amp;a_{3,n}&amp;\\cdots\\\\\n  &amp;\\cdots   &amp;  &amp;  &amp;  &amp; \\\\\n  &amp;a_{n,1}  &amp;a_{n,2}  &amp;a_{n,3}  &amp;\\cdots   &amp;a_{n,n}&amp;\\cdots\\\\\n  &amp;\\cdots   &amp;  &amp;  &amp;  &amp;\n\\end{matrix}\\\\\n(1)\u8bbeb_n=a_{n,n},\u6c42\u6570\u5217\\left \\{b_n  \\right \\} \u7684\u901a\u9879\u516c\u5f0f\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(2)\u8bbeS_n=a_{1,1}+a_{2,1}+\\cdots+a_{n,1},\u662f\u5426\u5b58\u5728\u5b9e\u6570\\lambda ,\u4f7fa_{n,1}\\le\\lambda S_n\u6052\u6210\u7acb\uff0c\u82e5\u5b58\u5728,~~~~~~~~~~\\\\\u6c42\u51fa\\lambda \u7684\u6240\u6709\u503c\uff0c\u82e5\u4e0d\u5b58\u5728\uff0c\u8bf4\u660e\u7406\u7531.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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\uff1a\\lambda = \\frac{3}{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-stackable-button-group stk-block-button-group stk-block stk-95dc1ba\" data-block-id=\"95dc1ba\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-button-group\">\n<div class=\"wp-block-stackable-button stk-block-button stk-block stk-c7f7dac\" data-block-id=\"c7f7dac\"><style>.stk-c7f7dac {border-top-left-radius:13px !important;border-top-right-radius:13px !important;border-bottom-right-radius:13px !important;border-bottom-left-radius:13px !important;overflow:hidden !important;}<\/style><a class=\"stk-link stk-button stk--hover-effect-darken\" href=\"http:\/\/jhwk.online\/?p=4642\" target=\"_blank\" rel=\"noreferrer noopener\"><span class=\"stk-button__inner-text\">\u89c2\u770b\u5fae\u8bfe<\/span><\/a><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u6709n^2(n\\ge 4)\u4e2a\u6b63\u6570\uff0c\u6392\u6210n\\times n\u77e9\u9635(n\u884cn\u5217\u7684\u6570\u8868)\uff1a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n\\begin{pmatrix}  \n  a_{11}&amp; a_{12}&amp; \\cdots  &amp; a_{1n} \\\\  \n  a_{21}&amp; a_{22}&amp; \\cdots  &amp; a_{2n} \\\\  \n  \\vdots &amp; \\vdots &amp; \\ddots &amp; \\vdots \\\\  \n  a_{n1}&amp; a_{n2}&amp; \\cdots  &amp; a_{nn}  \n\\end{pmatrix}  \\\\\n\u5176\u4e2d\u6bcf\u4e00\u884c\u7684\u6570\u6210\u7b49\u5dee\u6570\u5217\uff0c\u6bcf\u4e00\u5217\u7684\u6570\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u5e76\u4e14\u6240\u6709\u7684\u516c\u6bd4\u90fd\u76f8\u7b49\uff0c\u5df2\u77e5\\\\a_{24}=1,a_{42}=\\frac{1}{8} ,a_{43}=\\frac{3}{16}\n(1)\u6c42\u516c\u6bd4q;(2)\u7528k\u8868\u793aa_{4k};(3)\u6c42a_{11}+a_{22}+\\cdots +a_{nn}.~~~~~~~~~~<\/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\uff1a(1)q=\\frac{1}{2};(2)a_{4k}=\\frac{k}{16};(3)S=2-\\frac{n+2}{2^n}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/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-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","protected":false},"excerpt":{"rendered":"<p>\u9ad8\u8003\u771f\u9898\u3001\u5178\u578b\u95ee\u9898<\/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":[],"class_list":["post-1800","post","type-post","status-publish","format-standard","hentry","category-10"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1800","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=1800"}],"version-history":[{"count":1,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1800\/revisions"}],"predecessor-version":[{"id":4648,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/1800\/revisions\/4648"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1800"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}