{"id":6871,"date":"2021-10-21T21:28:58","date_gmt":"2021-10-21T15:58:58","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6871"},"modified":"2021-10-25T02:26:05","modified_gmt":"2021-10-24T20:56:05","slug":"if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/","title":{"rendered":"If \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)"},"content":{"rendered":"

Solution :<\/h2>\n

\\(\\because\\) \\(T_n\\) = \\(S_n – S_{n-1}\\)<\/p>\n

= \\({\\sum}_{r=1}^{n\u200e} T_r\\) – \\({\\sum}_{r=1}^{n\u200e – 1} T_r\\)<\/p>\n

= \\(n(n+1)(n+2)(n+3)\\over 8\\) – \\((n-1)(n)(n+1)(n+2)\\over 8\\)<\/p>\n

= \\(n(n+1)(n+2)\\over 8\\)[(n+3) – (n-1)] = \\(n(n+1)(n+2)\\over 8\\)(4)<\/p>\n

\\(T_n\\) = \\(n(n+1)(n+2)\\over 2\\)<\/p>\n

\\(\\implies\\) \\(1\\over T_n\\) = \\(2\\over n(n+1)(n+2)\\) = \\((n+2)-n\\over n(n+1)(n+2)\\)<\/p>\n

= \\(1\\over n(n+1)\\) – \\(1\\over (n+1)(n+2)\\)<\/p>\n

Let \\(V_n\\) = \\(1\\over n(n+1)\\)<\/p>\n

\\(\\therefore\\) \\(1\\over T_n\\) = \\(V_n\\) – \\(V_{n+1}\\)<\/p>\n

Putting n = 1, 2, 3, …… n<\/p>\n

\\(\\implies\\) \\(1\\over T_1\\) + \\(1\\over T_2\\) + \\(1\\over T_3\\) + ….. + \\(1\\over T_n\\) = \\(V_1\\) – \\(V_{n+1}\\)<\/p>\n

= \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\) = \\(n^2 + 3n\\over 2(n+1)(n+2)\\)<\/p>\n

\n

Similar Questions<\/h3>\n

Let \\(a_n\\) be the nth term of an AP. If \\(\\sum_{r=1}^{100}\\) \\(a_{2r}\\) = \\(\\alpha\\) and \\(\\sum_{r=1}^{100}\\) \\(a_{2r-1}\\) = \\(\\beta\\), then the common difference of the AP is<\/a><\/p>\n

Prove that the sum of first n natural numbers is \\(n(n+1)\\over 2\\)<\/a><\/p>\n

If \\((10)^9\\) + \\(2(11)^1(10)^8\\) + \\(3(11)^2(10)^7\\) + \u2026\u2026 + \\(10(11)^9\\) = \\(K(10)^9\\), then k is equal to<\/a><\/p>\n

If x, y and z are in AP and \\(tan^{-1}x\\), \\(tan^{-1}y\\) and \\(tan^{-1}z\\) are also in AP, then<\/a><\/p>\n

Find the sum of n terms of the series 1.3.5 + 3.5.7 + 5.7.9 + \u2026\u2026<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : \\(\\because\\) \\(T_n\\) = \\(S_n – S_{n-1}\\) = \\({\\sum}_{r=1}^{n\u200e} T_r\\) – \\({\\sum}_{r=1}^{n\u200e – 1} T_r\\) = \\(n(n+1)(n+2)(n+3)\\over 8\\) – \\((n-1)(n)(n+1)(n+2)\\over 8\\) = \\(n(n+1)(n+2)\\over 8\\)[(n+3) – (n-1)] = \\(n(n+1)(n+2)\\over 8\\)(4) \\(T_n\\) = \\(n(n+1)(n+2)\\over 2\\) \\(\\implies\\) \\(1\\over T_n\\) = \\(2\\over n(n+1)(n+2)\\) = \\((n+2)-n\\over n(n+1)(n+2)\\) = \\(1\\over n(n+1)\\) – \\(1\\over (n+1)(n+2)\\) Let \\(V_n\\) = \\(1\\over n(n+1)\\) \\(\\therefore\\) …<\/p>\n

If \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,57],"tags":[],"yoast_head":"\nIf \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)<\/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:\/\/mathemerize.com\/if-sum_r1n\u200e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n\u200e-1over-t_r\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)\" \/>\n<meta property=\"og:description\" content=\"Solution : (because) (T_n) = (S_n – S_{n-1}) = ({sum}_{r=1}^{n\u200e} T_r) – ({sum}_{r=1}^{n\u200e – 1} T_r) = (n(n+1)(n+2)(n+3)over 8) – ((n-1)(n)(n+1)(n+2)over 8) = (n(n+1)(n+2)over 8)[(n+3) – (n-1)] = (n(n+1)(n+2)over 8)(4) (T_n) = (n(n+1)(n+2)over 2) (implies) (1over T_n) = (2over n(n+1)(n+2)) = ((n+2)-nover n(n+1)(n+2)) = (1over n(n+1)) – (1over (n+1)(n+2)) Let (V_n) = (1over n(n+1)) (therefore) … If ({sum}_{r=1}^{n\u200e} T_r) = (nover 8) (n + 1)(n + 2)(n + 3), then find ({sum}_{r=1}^{n\u200e} )(1over T_r) Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/if-sum_r1n\u200e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n\u200e-1over-t_r\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-21T15:58:58+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T20:56:05+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\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\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"If \\\\({\\\\sum}_{r=1}^{n\u200e} T_r\\\\) = \\\\(n\\\\over 8\\\\) (n + 1)(n + 2)(n + 3), then find \\\\({\\\\sum}_{r=1}^{n\u200e} \\\\)\\\\(1\\\\over T_r\\\\)\",\"datePublished\":\"2021-10-21T15:58:58+00:00\",\"dateModified\":\"2021-10-24T20:56:05+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/\"},\"wordCount\":217,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Series Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/\",\"url\":\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/\",\"name\":\"If \\\\({\\\\sum}_{r=1}^{n\u200e} T_r\\\\) = \\\\(n\\\\over 8\\\\) (n + 1)(n + 2)(n + 3), then find \\\\({\\\\sum}_{r=1}^{n\u200e} \\\\)\\\\(1\\\\over T_r\\\\)\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-21T15:58:58+00:00\",\"dateModified\":\"2021-10-24T20:56:05+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"If \\\\({\\\\sum}_{r=1}^{n\u200e} T_r\\\\) = \\\\(n\\\\over 8\\\\) (n + 1)(n + 2)(n + 3), then find \\\\({\\\\sum}_{r=1}^{n\u200e} \\\\)\\\\(1\\\\over T_r\\\\)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"If \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)","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:\/\/mathemerize.com\/if-sum_r1n\u200e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n\u200e-1over-t_r\/","og_locale":"en_US","og_type":"article","og_title":"If \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)","og_description":"Solution : (because) (T_n) = (S_n – S_{n-1}) = ({sum}_{r=1}^{n\u200e} T_r) – ({sum}_{r=1}^{n\u200e – 1} T_r) = (n(n+1)(n+2)(n+3)over 8) – ((n-1)(n)(n+1)(n+2)over 8) = (n(n+1)(n+2)over 8)[(n+3) – (n-1)] = (n(n+1)(n+2)over 8)(4) (T_n) = (n(n+1)(n+2)over 2) (implies) (1over T_n) = (2over n(n+1)(n+2)) = ((n+2)-nover n(n+1)(n+2)) = (1over n(n+1)) – (1over (n+1)(n+2)) Let (V_n) = (1over n(n+1)) (therefore) … If ({sum}_{r=1}^{n\u200e} T_r) = (nover 8) (n + 1)(n + 2)(n + 3), then find ({sum}_{r=1}^{n\u200e} )(1over T_r) Read More »","og_url":"https:\/\/mathemerize.com\/if-sum_r1n\u200e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n\u200e-1over-t_r\/","og_site_name":"Mathemerize","article_published_time":"2021-10-21T15:58:58+00:00","article_modified_time":"2021-10-24T20:56:05+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"If \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)","datePublished":"2021-10-21T15:58:58+00:00","dateModified":"2021-10-24T20:56:05+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/"},"wordCount":217,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Series Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/","url":"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/","name":"If \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-21T15:58:58+00:00","dateModified":"2021-10-24T20:56:05+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/if-sum_r1n%e2%80%8e-t_r-nover-8-n-1n-2n-3-then-find-sum_r1n%e2%80%8e-1over-t_r\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"If \\({\\sum}_{r=1}^{n\u200e} T_r\\) = \\(n\\over 8\\) (n + 1)(n + 2)(n + 3), then find \\({\\sum}_{r=1}^{n\u200e} \\)\\(1\\over T_r\\)"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6871"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=6871"}],"version-history":[{"count":3,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6871\/revisions"}],"predecessor-version":[{"id":7436,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/6871\/revisions\/7436"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=6871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=6871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=6871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}