{"id":4642,"date":"2025-11-09T11:01:15","date_gmt":"2025-11-09T03:01:15","guid":{"rendered":"http:\/\/jhwk.online\/?p=4642"},"modified":"2025-11-10T19:58:22","modified_gmt":"2025-11-10T11:58:22","slug":"%e5%87%bd%e6%95%b0%e5%af%bc%e6%95%b03%e8%ae%b2%e8%a7%a3-3-2-2-2","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=4642","title":{"rendered":"\u6570\u5217\u7ecf\u5178\u95ee\u9898-3"},"content":{"rendered":"\n<div class=\"wp-block-stackable-subtitle stk-block-subtitle stk-block stk-8afe3d6\" data-block-id=\"8afe3d6\"><style>.stk-8afe3d6 .stk-block-subtitle__text{font-size:var(--stk--preset--font-size--medium, 20px) !important;color:#0693e3 !important;}@media screen and (max-width:999px){.stk-8afe3d6 .stk-block-subtitle__text{font-size:var(--stk--preset--font-size--medium, 20px) !important;}}<\/style><p class=\"stk-block-subtitle__text stk-subtitle has-text-color\">\u672c\u9898\u75312023\u7ea725\u73ed\u738b\u7389\u59ff\u8bb2\u89e3\uff01<\/p><\/div>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1920 \/ 1080;\" width=\"1920\" controls src=\"http:\/\/jhwk.online\/wp-content\/uploads\/2025\/11\/\u6570\u5217\u7ecf\u5178\u9898\u76ee3.mp4\"><\/video><\/figure>\n\n\n\n<p>[ratemypost]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-vivid-cyan-blue-color has-alpha-channel-opacity has-vivid-cyan-blue-background-color has-background is-style-wide\"\/>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-8a052dbd5caa870510f1e594e9e095cf\">\u9898\u76ee\u5c55\u793a\u2014\u2014\u5148\u63a2\u7a76\u3001\u518d\u542c\u8bb2<\/h5>\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<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color has-medium-font-size wp-elements-58b20738b8080c684d5fff23cf040d12\" style=\"color:#1e4b69;background:linear-gradient(0deg,rgb(230,242,255) 0%,rgb(230,242,255) 16%,rgb(92,175,230) 100%)\">\u89e3\u9898\u63a2\u7a76\u2014\u2014\u70b9\u51fb\u76f4\u8fbe<\/h4>\n\n\n\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left;\n    background-color: #e6f2ff; \/* \u6de1\u84dd\u8272\u80cc\u666f *\/\n    border: none;\n    padding: 8px 12px;\n    border-radius: 4px;\n    transition: all 0.3s ease; \/* \u5e73\u6ed1\u8fc7\u6e21\u52a8\u753b *\/\n    font-size: 16px;\n  }\n  \n  .video-jump-btn:hover {\n    background-color: #cce0ff; \/* \u7565\u6df1\u7684\u84dd\u8272\u80cc\u666f *\/\n    transform: scale(1.02); \/* \u8f7b\u5fae\u653e\u5927\u6548\u679c *\/\n    box-shadow: 0 2px 4px rgba(0,0,0,0.1); \/* \u589e\u52a0\u8f7b\u5fae\u9634\u5f71 *\/\n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime = 0; document.querySelector('video').play();\">\n\u95ee\u9898(1) \u7b2c\u4e00\u6b65\uff1a\u5206\u522b\u6c42\u51fa\\( d \\)\u3001\\( a_{1,1} \\)\u3001\\( q \\)\u7684\u503c\u5e76\u6c42\\( a_{n,n} \\)\n\uff1b\n<\/button>\n\n\n\n<br>\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime =220; document.querySelector('video').play();\">\n\n\u95ee\u9898(2) \u7b2c\u4e00\u6b65\uff1a\u6c42\u51fa\\( a_{n,1} \\)\u548c\\( S_{n} \\)\u540e\u4ee3\u5165\u539f\u4e0d\u7b49\u5f0f\uff1b\n\n<\/button>\n\n\n\n<br>\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime =330; document.querySelector('video').play();\">\n\n \u7b2c\u4e8c\u6b65\uff1a\u8ba8\u8bba\\( n \\)\u4e3a\u5076\u6570\u65f6$ \\lambda$\u7684\u8303\u56f4\uff1b\n\n\n<\/button>\n\n\n\n<br>\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime =457; document.querySelector('video').play();\">\n\n \u7b2c\u4e09\u6b65\uff1a\u8ba8\u8bba\\( n \\)\u4e3a\u5947\u6570\u65f6$ \\lambda$\u7684\u8303\u56f4\u3002\n\n<\/button>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848\u89e3\u6790<\/summary>\n \n\n\n\n(1) \u6c42\u6570\u5217$\\{ b_{n}\\}$\u7684\u901a\u9879\u516c\u5f0f <p>\u8bbe\u7b2c\u4e00\u884c\u7b49\u5dee\u6570\u5217\u7684\u516c\u5dee\u4e3a$d$\uff0c\u7b49\u6bd4\u6570\u5217\u7684\u516c\u6bd4\u4e3a$q$\u3002<\/p> <p>&#8211; \u7531$a_{1,3}=5$\uff0c\u5f97$a_{1,1}+2d = 5$\u3002<\/p> <p>&#8211; \u7531$a_{2,2}=-6$\uff0c\u5f97$(a_{1,1}+d)q = -6$\u3002<\/p> <p>&#8211; \u7531$a_{4,2}^{2}=a_{7,5}$\uff0c\u5f97$[(a_{1,1}+d)q^{3}]^{2}=(a_{1,1}+4d)q^{6}$\uff0c\u5316\u7b80\u5f97$(a_{1,1}+d)^{2}=a_{1,1}+4d$\u3002<\/p> <p>\u5c06$a_{1,1}=5 &#8211; 2d$\u4ee3\u5165$(a_{1,1}+d)^{2}=a_{1,1}+4d$\uff0c\u5f97$(5 &#8211; d)^{2}=5 + 2d$\uff0c\u5373$d^{2}-12d + 20 = 0$\uff0c\u89e3\u5f97$d = 2$\u6216$d = 10$\u3002<\/p> <p>\u5f53$d = 10$\u65f6\uff0c$a_{1,1}=5 &#8211; 20 = -15 < 0$\uff08\u4e0e$a_{1,1}>0$\u77db\u76fe\uff0c\u820d\u53bb\uff09\u3002\u6545$d = 2$\uff0c$a_{1,1}=5 &#8211; 4 = 1$\u3002<\/p> <p>\u5c06$a_{1,1}=1$\uff0c$d = 2$\u4ee3\u5165$(a_{1,1}+d)q = -6$\uff0c\u5f97$3q = -6$\uff0c\u89e3\u5f97$q = -2$\u3002<\/p> <p>\u56e0\u4e3a$a_{n,n}=a_{1,n}q^{n &#8211; 1}=[a_{1,1}+(n &#8211; 1)d]q^{n &#8211; 1}$\uff0c\u4ee3\u5165$a_{1,1}=1$\uff0c$d = 2$\uff0c$q = -2$\uff0c\u5f97$b_{n}=a_{n,n}=(2n &#8211; 1)\\cdot (-2)^{n &#8211; 1}$\u3002<\/p>  (2) \u6c42\u5b9e\u6570$\\lambda$\u7684\u503c <p>\u5148\u6c42$a_{n,1}$\u548c$S_{n}$\uff1a<\/p> <p>$a_{n,1}=a_{1,1}q^{n &#8211; 1}=(-2)^{n &#8211; 1}$\uff1b<\/p> <p>$S_{n}=a_{1,1}+a_{2,1}+\\cdots +a_{n,1}=\\displaystyle \\frac{1 &#8211; (-2)^{n}}{1 + 2}=\\displaystyle \\frac{1 &#8211; (-2)^{n}}{3}$\u3002<\/p> <p>\u7531$a_{n,1}\\leq \\lambda S_{n}$\uff0c\u5f97$(-2)^{n &#8211; 1}\\leq \\lambda \\cdot \\displaystyle \\frac{1 &#8211; (-2)^{n}}{3}$\uff0c\u5373$3\\cdot (-2)^{n &#8211; 1}\\leq \\lambda [1 &#8211; (-2)^{n}]$\u3002<\/p> <p>\u2460 \u5f53$n$\u4e3a\u5076\u6570\u65f6\uff0c\u539f\u5f0f\u5316\u4e3a$-3\\cdot 2^{n &#8211; 1}\\leq \\lambda (1 &#8211; 2^{n})$\uff0c\u5373$3\\cdot 2^{n &#8211; 1}\\leq \\lambda (2^{n} &#8211; 1)$\uff0c\u5219$\\lambda \\geq \\displaystyle \\frac{3\\cdot 2^{n &#8211; 1}}{2^{n} &#8211; 1}$\u3002<\/p> <p>\u5bf9$\\displaystyle \\frac{3\\cdot 2^{n &#8211; 1}}{2^{n} &#8211; 1}$\u53d8\u5f62\uff1a$\\displaystyle \\frac{3\\cdot 2^{n &#8211; 1}}{2^{n} &#8211; 1}=\\displaystyle \\frac{\\displaystyle \\frac{3}{2}\\cdot 2^{n}}{\\displaystyle \\frac{3}{2}\\cdot 2^{n} &#8211; \\displaystyle \\frac{3}{2}}=\\displaystyle \\frac{3}{2}+\\displaystyle \\frac{3}{2(2^{n} &#8211; 1)}$\u3002<\/p> <p>\u56e0\u4e3a$\\displaystyle \\frac{3}{2}+\\displaystyle \\frac{3}{2(2^{n} &#8211; 1)}<\\displaystyle \\frac{3}{2}$\uff0c\u6240\u4ee5$\\lambda \\leq \\displaystyle \\frac{3}{2}$\u3002<\/p> <p>\u2461 \u5f53$n$\u4e3a\u5947\u6570\u65f6\uff0c\u539f\u5f0f\u5316\u4e3a$3\\cdot 2^{n &#8211; 1}\\leq \\lambda (1 + 2^{n})$\uff0c\u5219$\\lambda \\geq \\displaystyle \\frac{3\\cdot 2^{n &#8211; 1}}{1 + 2^{n}}$\u3002<\/p> <p>\u5bf9$\\displaystyle \\frac{3\\cdot 2^{n &#8211; 1}}{1 + 2^{n}}$\u53d8\u5f62\uff1a$\\displaystyle \\frac{3\\cdot 2^{n &#8211; 1}}{1 + 2^{n}}=\\displaystyle \\frac{\\displaystyle \\frac{3}{2}\\cdot 2^{n}}{\\displaystyle \\frac{3}{2}\\cdot 2^{n} + \\displaystyle \\frac{3}{2}}=\\displaystyle \\frac{3}{2}-\\displaystyle \\frac{3}{2(1 + 2^{n})}$\u3002<\/p> <p>\u56e0\u4e3a$\\displaystyle \\frac{3}{2}-\\displaystyle \\frac{3}{2(1 + 2^{n})}<\\displaystyle \\frac{3}{2}$\uff0c\u6240\u4ee5$\\lambda \\geq \\displaystyle \\frac{3}{2}$\u3002<\/p> <p>\u7efc\u4e0a\uff0c$\\lambda = \\displaystyle \\frac{3}{2}$\u3002<\/p>\n<\/details>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u9898\u75312023\u7ea725\u73ed\u738b\u7389\u59ff\u8bb2\u89e3\uff01 [ratemypost] \u9898\u76ee\u5c55\u793a\u2014\u2014\u5148\u63a2\u7a76\u3001\u518d\u542c\u8bb2 \u89e3\u9898\u63a2\u7a76\u2014\u2014\u70b9\u51fb\u76f4\u8fbe [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4642","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4642","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=4642"}],"version-history":[{"count":5,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4642\/revisions"}],"predecessor-version":[{"id":4700,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4642\/revisions\/4700"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4642"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4642"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4642"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}