{"id":28844,"date":"2021-09-10T20:50:13","date_gmt":"2021-09-10T15:20:13","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=28844"},"modified":"2021-10-22T09:06:18","modified_gmt":"2021-10-22T03:36:18","slug":"02-09-02-q1","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/02-09-02-q1\/","title":{"rendered":"\u0dc3\u0dd2\u0dad\u0db1\u0dca\u0db1\u0da7 \u0dba\u0db8\u0d9a\u0dca\u2026.."},"content":{"rendered":"\n<div class=\"wp-block-cover has-background-dim\" style=\"background-color:#e0c8f8\"><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#000532;font-size:25px\"><strong>\u0dc3\u0dd2\u0dad\u0db1\u0dca\u0db1\u0da7 \u0dba\u0db8\u0d9a\u0dca\u2026..<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color\" style=\"color:#000532;font-size:25px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac x1+\\frac x{1+2}+\\frac x{1+2+3}+\u2026+\\frac x{1+2+\u2026+4041}=4041\\;\\text{\u0dc0\u0dd2\u0dc3\u0db3\u0db1\u0dca\u0db1.}<\/span><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}{\\mathrm U}_{\\mathrm r}\\;&amp;=&amp;\\;1\\;+\\;2\\;+\\;3\\;+.......+\\;\\mathrm r\\;\\text{ \u0dc1\u0dca\u200d\u0dbb\u0dda\u0dab\u0dd2\u0dba\u0dda \u0db4\u0daf r\u00a0\u00a0\u0dc4\u0dd2 \u0d93\u0d9a\u0dca\u200d\u0dba}\\\\&amp;=&amp;\\frac{\\mathrm r\\;(1+\\;\\mathrm r\\;)}2\\end{array}<\/span>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\text{(\u0db4\u0ddc\u0daf\u0dd4\u00a0\u0d85\u0db1\u0dca\u0dad\u0dbb\u0dba\u00a01\u00a0\u0dc0\u0dd6\u0daf\u00a0\u0db4\u0dc5\u0db8\u0dd4\u00a0\u0db4\u0daf\u0dba\u00a01\u00a0\u0dc0\u0dd6\u0daf\u00a0\u0dc3\u0db8\u0dcf\u0db1\u0dca\u0dad\u0dbb\u00a0\u0dc1\u0dca\u200d\u0dbb\u0dda\u0dab\u0dd2\u0dba\u0d9a\u00a0\u0db4\u0daf\u00a0r\u00a0\u0dc4\u0dd2\u00a0\u0d93\u0d9a\u0dca\u200d\u0dba\u00a0Sr\u00a0=\u00a0\u0db4\u0daf\u00a0\u0d9c\u0dab\u0db1(\u0d86\u0dbb\u0db8\u0dca\u0db7\u0d9a\u00a0\u0db4\u0daf\u0dba+\u0d85\u0dc0\u0dc3\u0dcf\u0db1\u00a0\u0db4\u0daf\u0dba)\/2\u00a0\u0db8\u0d9f\u0dd2\u0db1\u0dca\u00a0\u0dbd\u0dd0\u0db6\u0dda.)}\\\\\\\\\\mathrm{\u0db4\u0ddc\u0daf\u0dd4}\\;\\mathrm{\u0db4\u0daf\u0dba}\\;\\;=\\;\\frac{\\mathrm x}{{\\mathrm U}_{\\mathrm r}}\\;=\\;\\frac{2\\mathrm x}{\\mathrm r(\\mathrm r\\;+\\;1)}\\;=\\;2\\mathrm x\\frac{(\\mathrm r\\;+\\;1)-\\;\\mathrm r}{\\mathrm r(\\mathrm r\\;+\\;1)}\\;=\\;\\frac{2\\mathrm x}{\\mathrm r}\\;=\\;\\frac{2\\mathrm x}{\\mathrm r\\;+\\;1}\\;=\\;\\mathrm f\\;(\\mathrm r)\\;-\\;\\mathrm f(\\mathrm r\\;+\\;1)\\end{array}<\/span>\r\n<p>&nbsp;<\/p>\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\overset{4041}{\\underset{\\mathrm r\\;=\\;1}{\\sum\\;\\;}}\\;\\frac{\\displaystyle\\mathrm x}{\\displaystyle{\\mathrm U}_{\\mathrm r}}\\;&amp;=&amp;\\;\\overset{4041}{\\underset{\\mathrm r\\;=\\;1}{\\sum\\;\\;}}\\;\\mathrm f(\\mathrm r)\\;-\\;\\mathrm f(\\mathrm r+1)\\\\&amp;=&amp;\\;\\mathrm f(1)\\;-\\;\\mathrm f(2)\\\\&amp;=&amp;\\;\\mathrm f(2)\\;-\\;\\mathrm f(3)\\\\&amp;&amp;.\\\\&amp;&amp;.\\\\&amp;&amp;.\\\\&amp;=&amp;\\;\\mathrm f(4041)\\;-\\;\\mathrm f(4042)\\\\&amp;&amp;.................................\\\\&amp;&amp;\\\\\\overset{4041}{\\underset{\\mathrm r\\;=\\;1}{\\sum\\;\\;}}\\;\\frac{\\mathrm x}{{\\mathrm U}_{\\mathrm r}}\\;&amp;=&amp;\\;\\mathrm f(1)\\;-\\;\\mathrm f(2)\\\\[4px]4041\\;\\;&amp;=&amp;\\;2\\mathrm x\\;-\\;\\frac{2\\mathrm x}{4042}\\\\[4px]4041\\;&amp;=&amp;\\;2\\mathrm x\\;\\left(\\frac{4042}{4042}\\;-\\;\\frac1{4042}\\right)\\\\[4px]4041\\;&amp;=&amp;\\;2\\mathrm x\\;\\left(\\frac{\\displaystyle4041}{\\displaystyle4042}\\right)\\\\2x\\;&amp;=&amp;\\;4042\\\\x\\;&amp;=&amp;\\;2021\\end{array}<\/span>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":121,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[6067,42,3629],"tags":[],"class_list":{"0":"post-28844","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-infinite-thinking","7":"category-advanced-level-science","8":"category-combined-mathematics"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/28844"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/121"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=28844"}],"version-history":[{"count":10,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/28844\/revisions"}],"predecessor-version":[{"id":33587,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/28844\/revisions\/33587"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=28844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=28844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=28844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}