{"id":28836,"date":"2021-09-10T22:01:48","date_gmt":"2021-09-10T16:31:48","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=28836"},"modified":"2021-10-22T09:02:54","modified_gmt":"2021-10-22T03:32:54","slug":"02-09-01-q1","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/02-09-01-q1\/","title":{"rendered":"\u0dc1\u0dca\u200d\u0dbb\u0dda\u0dab\u0dd2\u0dba\u0dda \u0d93\u0d9a\u0dca\u200d\u0dba \u0d91\u0d9a\u0dc0\u0dbb \u0dbd\u0dd2\u0dba\u0db1\u0dca\u0db1 \u0d94\u0dba\u0dcf\u0da7\u0dad\u0dca \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca\u0daf?"},"content":{"rendered":"\n<p>&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-background\" style=\"background-color:#e0c8f8;color:#000532;font-size:20px\"><span class=\"wp-katex-eq\" data-display=\"false\">\\frac1{1+\\sqrt2}+\\frac1{\\sqrt2+\\sqrt3}+\\frac1{\\sqrt3{+}{\\sqrt4}}+\\frac1{\\sqrt4{+}{\\sqrt5}}+\u2026+\\frac1{\\sqrt{2020}+\\sqrt{2021}}=4041<\/span><br>\u0dc1\u0dca\u200d\u0dbb\u0dda\u0dab\u0dd2\u0dba\u0dda \u0d93\u0d9a\u0dca\u200d\u0dba \u0d91\u0d9a\u0dc0\u0dbb \u0dbd\u0dd2\u0dba\u0db1\u0dca\u0db1 \u0d94\u0dba\u0dcf\u0da7\u0dad\u0dca \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca\u0daf?<\/p>\n\n\n\n<div class=\"wp-block-buttons aligncenter is-layout-flex wp-block-buttons-is-layout-flex\">\n<\/div>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac{\\displaystyle1}{\\displaystyle1+\\;\\sqrt2}\\;+\\;\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt2+\\;\\sqrt3}\\;+\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt3+\\;\\sqrt4}\\;+\\;\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt4+\\;\\sqrt5}\\;+\\;...................+\\;\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt{2020}+\\;\\sqrt{2021}}\\;\\text{\u0dc1\u0dca\u200d\u0dbb\u0dda\u0dab\u0dd2\u0dba \u0dc3\u0dbd\u0d9a\u0db8\u0dd4.}\\\\\\text{\u0db4\u0ddc\u0daf\u0dd4 \u0db4\u0daf\u0dba \u0dc3\u0ddc\u0dba\u0db8\u0dd4.}\\\\{\\mathrm U}_{\\mathrm k}\\;=\\;\\;\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt{\\mathrm k}+\\;\\sqrt{\\mathrm k+1}}\\\\\\end{array}<\/span>\r\n<p style=\"text-align: left\">\u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0db6\u0daf\u0dca\u0db0\u0dba\u0dd9\u0db1\u0dca \u0d9c\u0dd4\u0dab \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dd9\u0db1\u0dca ,<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt{\\mathrm k}+\\;\\sqrt{\\mathrm k+1}}\\;&amp;=&amp;\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt{\\mathrm k}+\\;\\sqrt{\\mathrm k+1}}\\;\\times\\frac{\\sqrt{\\mathrm k+1}{\\displaystyle\\;}{\\displaystyle-}{\\displaystyle\\;}{\\displaystyle\\sqrt{\\mathrm k}}}{\\sqrt{\\mathrm k+1}{\\displaystyle\\;}{\\displaystyle-}{\\displaystyle\\;}{\\displaystyle\\sqrt{\\mathrm k}}}\\\\\\;\\;\\;\\;\\;\\;\\;&amp;=&amp;\\frac{\\sqrt{\\mathrm k+1}{\\displaystyle\\;}{\\displaystyle-}{\\displaystyle\\;}{\\displaystyle\\sqrt{\\mathrm k}}}{(\\mathrm k\\;+\\;1)\\;-\\;\\mathrm k}\\\\{\\mathrm U}_{\\mathrm k}\\;\\;&amp;=&amp;\\;-\\sqrt{\\mathrm k}\\;+\\;\\sqrt{\\mathrm k+1}\\\\\\frac{\\displaystyle1}{\\displaystyle1+\\;\\sqrt2}\\;+\\;\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt2+\\;\\sqrt3}\\;+\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt3+\\;\\sqrt4}\\;+\\;\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt4+\\;\\sqrt5}\\;+\\;...................+\\;\\frac{\\displaystyle1}{\\displaystyle\\;\\sqrt{2020}+\\;\\sqrt{2021}}\\;\\;&amp;=&amp;\\;\\left(-\\sqrt1\\;+\\;\\sqrt2\\right)\\;+\\;\\left(-\\sqrt2\\;+\\;\\sqrt3\\right)\\;+\\;\\left(-\\sqrt3\\;+\\;\\sqrt4\\right)\\;+........+\\left(-\\sqrt{2020}\\;+\\;\\sqrt{2021}\\right)\\\\&amp;=&amp;\\;\\underline{-1\\;+\\;\\sqrt{2021}}\\\\&amp;&amp;\\end{array}<\/span><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; \u0dc1\u0dca\u200d\u0dbb\u0dda\u0dab\u0dd2\u0dba\u0dda \u0d93\u0d9a\u0dca\u200d\u0dba \u0d91\u0d9a\u0dc0\u0dbb \u0dbd\u0dd2\u0dba\u0db1\u0dca\u0db1 \u0d94\u0dba\u0dcf\u0da7\u0dad\u0dca \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca\u0daf?<\/p>\n","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-28836","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\/28836"}],"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=28836"}],"version-history":[{"count":19,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/28836\/revisions"}],"predecessor-version":[{"id":33588,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/28836\/revisions\/33588"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=28836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=28836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=28836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}