{"id":14490,"date":"2020-12-11T07:31:09","date_gmt":"2020-12-11T02:01:09","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=14490"},"modified":"2020-12-11T09:20:31","modified_gmt":"2020-12-11T03:50:31","slug":"binomial-theorem-index","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/binomial-theorem-index\/","title":{"rendered":"Binomial Theorem for any Index"},"content":{"rendered":"<h2>Binomial Theorem for any Index<\/h2>\n<p>https:\/\/www.youtube.com\/watch?v=xMziTBR34_M<\/p>\n<h3>Binomial theorem for positive integral index<\/h3>\n<p>The rule by which any power of binomial can be expanded is called the binomial theorem.<br \/>\nIf n is a positive integer and x, y \u2208\u00a0C then<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-130391\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg\" alt=\"Binomial Theorem for any Index 1\" width=\"597\" height=\"257\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg 597w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1-300x129.jpg 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<h3>Binomial theorem for any Index<\/h3>\n<p><strong>Statement :<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-130392\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-2.jpg\" alt=\"Binomial Theorem for any Index 2\" width=\"516\" height=\"118\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-2.jpg 516w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-2-300x69.jpg 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><br \/>\nwhen n is a negative integer or a fraction, where , otherwise expansion will not be possible.<br \/>\nIf first term is not 1, then make first term unity in the following way,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-130393\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-3.jpg\" alt=\"Binomial Theorem for any Index 3\" width=\"301\" height=\"66\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-3.jpg 301w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-3-300x66.jpg 300w\" sizes=\"(max-width: 301px) 100vw, 301px\" \/><\/p>\n<h3><strong>General term :<\/strong><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-130394\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-4.jpg\" alt=\"Binomial Theorem for any Index 4\" width=\"329\" height=\"53\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-4.jpg 329w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-4-300x48.jpg 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<h3>Some important expansions<\/h3>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-130415\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-5.jpg\" alt=\"Binomial Theorem for any Index 5\" width=\"546\" height=\"728\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-5.jpg 546w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-5-225x300.jpg 225w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<h3>Problems on approximation by the binomial theorem :<\/h3>\n<p>We have,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-130416\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-6.jpg\" alt=\"Binomial Theorem for any Index 6\" width=\"328\" height=\"55\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-6.jpg 328w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-6-300x50.jpg 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nIf <em>x<\/em> is small compared with 1, we find that the values of x<sup>2<\/sup>, x<sup>3<\/sup>, x<sup>4<\/sup>, \u2026.. become smaller and smaller.<br \/>\n\u2234 The terms in the above expansion become smaller and smaller. If <em>x<\/em> is very small compared with 1, we might take 1 as a first approximation to the value of (1 + x)<sup>n<\/sup> or (1 + nx) as a second approximation.<\/p>\n<h3>Three \/ Four consecutive terms or Coefficients<\/h3>\n<p>(1) <strong>If consecutive coefficients are given:<\/strong> In this case divide consecutive coefficients pair wise. We get equations and then solve them.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-130417\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-7.jpg\" alt=\"Binomial Theorem for any Index 7\" width=\"600\" height=\"152\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-7.jpg 600w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-7-300x76.jpg 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<h3>Some important points<\/h3>\n<p><strong>(1) Pascal&#8217;s Triangle<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-130418\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-8.jpg\" alt=\"Binomial Theorem for any Index 8\" width=\"499\" height=\"230\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-8.jpg 499w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-8-300x138.jpg 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\nPascal&#8217;s triangle gives the direct binomial coefficients.<br \/>\n<em>Example :<\/em> (x + y)<sup>4<\/sup> = x<sup>4<\/sup> + 4x<sup>3<\/sup>y + 6x<sup>2<\/sup>y<sup>2<\/sup> + 4xy<sup>3<\/sup> + y<sup>4<\/sup>.<\/p>\n<p><strong>(2)<\/strong> <strong>Method for finding terms free from radicals or rational terms in the expansion of (a<sup>1\/p<\/sup> + b<sup>1\/q<\/sup>)<sup>N<\/sup> <\/strong><strong>\u2200 a, b \u2208 prime numbers:<\/strong><br \/>\nFind the general term<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-130419\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-9.jpg\" alt=\"Binomial Theorem for any Index 9\" width=\"344\" height=\"56\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-9.jpg 344w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-9-300x49.jpg 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><br \/>\nPutting the values of 0 \u2264 r \u2264 N, when indices of a and b are integers.<br \/>\nNumber of irrational terms = Total terms \u2013 Number of rational terms.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Binomial Theorem for any Index https:\/\/www.youtube.com\/watch?v=xMziTBR34_M Binomial theorem for positive integral index The rule by which any power of binomial can be expanded is called the binomial theorem. If n is a positive integer and x, y \u2208\u00a0C then Binomial theorem for any Index Statement : when n is a negative integer or a fraction, &#8230; <a title=\"Binomial Theorem for any Index\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/binomial-theorem-index\/\" aria-label=\"More on Binomial Theorem for any Index\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[5572,5571,5575,5573,5574],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Binomial Theorem for any Index - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/binomial-theorem-index\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binomial Theorem for any Index\" \/>\n<meta property=\"og:description\" content=\"Binomial Theorem for any Index https:\/\/www.youtube.com\/watch?v=xMziTBR34_M Binomial theorem for positive integral index The rule by which any power of binomial can be expanded is called the binomial theorem. If n is a positive integer and x, y \u2208\u00a0C then Binomial theorem for any Index Statement : when n is a negative integer or a fraction, ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/cbselibrary.com\/binomial-theorem-index\/\" \/>\n<meta property=\"og:site_name\" content=\"CBSE Library\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2020-12-11T02:01:09+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-12-11T03:50:31+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/cbselibrary.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/cbselibrary.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/cbselibrary.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/cbselibrary.com\/#website\",\"url\":\"https:\/\/cbselibrary.com\/\",\"name\":\"CBSE Library\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/cbselibrary.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/cbselibrary.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg\",\"contentUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg\",\"width\":597,\"height\":257,\"caption\":\"Binomial Theorem for any Index 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#webpage\",\"url\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/\",\"name\":\"Binomial Theorem for any Index - CBSE Library\",\"isPartOf\":{\"@id\":\"https:\/\/cbselibrary.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#primaryimage\"},\"datePublished\":\"2020-12-11T02:01:09+00:00\",\"dateModified\":\"2020-12-11T03:50:31+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/cbselibrary.com\/binomial-theorem-index\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/cbselibrary.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Binomial Theorem for any Index\"}]},{\"@type\":\"Article\",\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#webpage\"},\"author\":{\"@id\":\"https:\/\/cbselibrary.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794\"},\"headline\":\"Binomial Theorem for any Index\",\"datePublished\":\"2020-12-11T02:01:09+00:00\",\"dateModified\":\"2020-12-11T03:50:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#webpage\"},\"wordCount\":255,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/cbselibrary.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg\",\"keywords\":[\"Binomial Theorem for any Index\",\"Binomial theorem for positive integral index\",\"Pascal's Triangle\",\"Problems on approximation by the binomial theorem\",\"Three \/ Four consecutive terms or Coefficients\"],\"articleSection\":[\"Mathematics\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/cbselibrary.com\/binomial-theorem-index\/#respond\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/cbselibrary.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/cbselibrary.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Binomial Theorem for any Index - CBSE Library","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/cbselibrary.com\/binomial-theorem-index\/","og_locale":"en_US","og_type":"article","og_title":"Binomial Theorem for any Index","og_description":"Binomial Theorem for any Index https:\/\/www.youtube.com\/watch?v=xMziTBR34_M Binomial theorem for positive integral index The rule by which any power of binomial can be expanded is called the binomial theorem. If n is a positive integer and x, y \u2208\u00a0C then Binomial theorem for any Index Statement : when n is a negative integer or a fraction, ... Read more","og_url":"https:\/\/cbselibrary.com\/binomial-theorem-index\/","og_site_name":"CBSE Library","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2020-12-11T02:01:09+00:00","article_modified_time":"2020-12-11T03:50:31+00:00","og_image":[{"url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg"}],"twitter_card":"summary","twitter_misc":{"Written by":"Prasanna","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/cbselibrary.com\/#organization","name":"Aplus Topper","url":"https:\/\/cbselibrary.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/#logo","inLanguage":"en-US","url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/cbselibrary.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/cbselibrary.com\/#website","url":"https:\/\/cbselibrary.com\/","name":"CBSE Library","description":"Improve your Grades","publisher":{"@id":"https:\/\/cbselibrary.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/cbselibrary.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#primaryimage","inLanguage":"en-US","url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg","contentUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg","width":597,"height":257,"caption":"Binomial Theorem for any Index 1"},{"@type":"WebPage","@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#webpage","url":"https:\/\/cbselibrary.com\/binomial-theorem-index\/","name":"Binomial Theorem for any Index - CBSE Library","isPartOf":{"@id":"https:\/\/cbselibrary.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#primaryimage"},"datePublished":"2020-12-11T02:01:09+00:00","dateModified":"2020-12-11T03:50:31+00:00","breadcrumb":{"@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/cbselibrary.com\/binomial-theorem-index\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/cbselibrary.com\/"},{"@type":"ListItem","position":2,"name":"Binomial Theorem for any Index"}]},{"@type":"Article","@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#article","isPartOf":{"@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#webpage"},"author":{"@id":"https:\/\/cbselibrary.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794"},"headline":"Binomial Theorem for any Index","datePublished":"2020-12-11T02:01:09+00:00","dateModified":"2020-12-11T03:50:31+00:00","mainEntityOfPage":{"@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#webpage"},"wordCount":255,"commentCount":0,"publisher":{"@id":"https:\/\/cbselibrary.com\/#organization"},"image":{"@id":"https:\/\/cbselibrary.com\/binomial-theorem-index\/#primaryimage"},"thumbnailUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2017\/05\/Binomial-Theorem-for-any-Index-1.jpg","keywords":["Binomial Theorem for any Index","Binomial theorem for positive integral index","Pascal's Triangle","Problems on approximation by the binomial theorem","Three \/ Four consecutive terms or Coefficients"],"articleSection":["Mathematics"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/cbselibrary.com\/binomial-theorem-index\/#respond"]}]},{"@type":"Person","@id":"https:\/\/cbselibrary.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/cbselibrary.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts\/14490"}],"collection":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/comments?post=14490"}],"version-history":[{"count":0,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts\/14490\/revisions"}],"wp:attachment":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/media?parent=14490"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/categories?post=14490"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/tags?post=14490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}