{"id":2271,"date":"2021-06-26T12:29:15","date_gmt":"2021-06-26T16:29:15","guid":{"rendered":"https:\/\/josmfs.net\/?p=2271"},"modified":"2021-08-20T18:15:14","modified_gmt":"2021-08-20T22:15:14","slug":"surprising-identity","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/06\/26\/surprising-identity\/","title":{"rendered":"Surprising Identity"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2268\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Surprising-Identity-Fig2.jpg\" alt=\"\" width=\"209\" height=\"150\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Surprising-Identity-Fig2.jpg 425w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Surprising-Identity-Fig2-300x215.jpg 300w\" sizes=\"auto, (max-width: 209px) 100vw, 209px\" \/>Here is surprising problem from the 1875 <em>The<\/em> <em>Analyst<\/em><\/p>\n<p><strong>\u201c81<\/strong>. By G. W. Hill, Nyack Turnpike, N. Y. \u2014 Prove that, <em>identically<\/em>,<img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2270\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Surprising-Identity.jpg\" alt=\"\" width=\"368\" height=\"45\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Surprising-Identity.jpg 713w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Surprising-Identity-300x37.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Surprising-Identity-624x76.jpg 624w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/p>\n<p>\u201d<\/p>\n<p>By \u201cidentically\u201d the proposer means for all <em>n<\/em> = 1, 2, 3, \u2026.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/06\/Surprising-Identity-210518.pdf\">Surprising Identity<\/a><\/p>\n<p><strong>(Update 8\/20\/2021)<\/strong>\u00a0 James Propp at his website has an informative, extensive <a href=\"https:\/\/mathenchant.wordpress.com\/2021\/08\/16\/reckoning-and-reasoning\/#more-4128\">article<\/a> on mathematical induction and its variations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is surprising problem from the 1875 The Analyst \u201c81. By G. W. Hill, Nyack Turnpike, N. Y. \u2014 Prove that, identically, \u201d By \u201cidentically\u201d the proposer means for all n = 1, 2, 3, \u2026. See the Surprising Identity (Update 8\/20\/2021)\u00a0 James Propp at his website has an informative, extensive article on mathematical induction [&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":[104,218],"class_list":["post-2271","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-mathematical-induction","tag-the-analyst"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2271","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=2271"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2271\/revisions"}],"predecessor-version":[{"id":2338,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2271\/revisions\/2338"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2271"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2271"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2271"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}