{"id":2714,"date":"2022-06-04T08:12:45","date_gmt":"2022-06-04T12:12:45","guid":{"rendered":"https:\/\/josmfs.net\/?p=2714"},"modified":"2024-04-06T13:16:12","modified_gmt":"2024-04-06T17:16:12","slug":"a-nice-factorial-sum","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/06\/04\/a-nice-factorial-sum\/","title":{"rendered":"A Nice Factorial Sum"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2712\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/06\/Nice-Factorial-Sum-Fig2.jpg\" alt=\"\" width=\"200\" height=\"202\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/06\/Nice-Factorial-Sum-Fig2.jpg 402w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/06\/Nice-Factorial-Sum-Fig2-296x300.jpg 296w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is another infinite series from <a href=\"https:\/\/mindyourdecisions.com\/blog\/2021\/10\/04\/a-nice-factorial-sum-from-france\/\">Presh Talwalkar<\/a>, but with a twist.<\/p>\n<p>\u201cThis problem is adapted from one given in an annual national math competition exam in France. Evaluate the infinite series:<\/p>\n<p style=\"text-align: center;\">1\/2! + 2\/3! + 3\/4! + \u2026\u201d<\/p>\n<p>The twist is that Talwalkar provides three solutions, illustrating three different techniques that I in fact have used before in series and sequence problems.\u00a0 But this time I actually found a simpler solution that avoids all these.\u00a0 You also need to remember what a factorial is: <em>n<\/em>! =<em>n<\/em>(<em>n<\/em> \u2013 1)(<em>n<\/em> \u2013 2)\u20263\u00b72\u00b71.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Nice-Factorial-Sum-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See a <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/06\/Nice-Factorial-Sum-211018.pdf\">Nice Factorial Sum<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is another infinite series from Presh Talwalkar, but with a twist. \u201cThis problem is adapted from one given in an annual national math competition exam in France. Evaluate the infinite series: 1\/2! + 2\/3! + 3\/4! + \u2026\u201d The twist is that Talwalkar provides three solutions, illustrating three different techniques that I in fact [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[17,230],"class_list":["post-2714","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-presh-talwalkar","tag-sequences-and-series"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2714","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2714"}],"version-history":[{"count":5,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2714\/revisions"}],"predecessor-version":[{"id":3615,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2714\/revisions\/3615"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2714"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2714"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2714"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}