{"id":915,"date":"2019-04-13T10:21:21","date_gmt":"2019-04-13T14:21:21","guid":{"rendered":"http:\/\/josmfs.net\/?p=915"},"modified":"2024-04-14T10:45:06","modified_gmt":"2024-04-14T14:45:06","slug":"infinite-product-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/04\/13\/infinite-product-problem\/","title":{"rendered":"Infinite Product Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-918\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/04\/Infinite-Product-Prob-Fig3.jpg\" alt=\"\" width=\"100\" height=\"117\" \/>This is a challenging problem from <em>Mathematical Quickies<\/em> (1967).<\/p>\n<p>\u201cEvaluate the infinite product:<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-912 alignnone\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/04\/Infinite-Product-Eq.jpg\" alt=\"\" width=\"219\" height=\"30\" \/>&#8221;<\/p>\n<p>I came up with a motivated solution using some standard techniques from calculus. <em>Mathematical Quickies<\/em> had a solution that did not employ calculus, but one which I felt used unmotivated tricks.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Infinite-Product-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/04\/Infinite-Product-Problem-190307.pdf\">Infinite Product Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a challenging problem from Mathematical Quickies (1967). \u201cEvaluate the infinite product:&#8221; I came up with a motivated solution using some standard techniques from calculus. Mathematical Quickies had a solution that did not employ calculus, but one which I felt used unmotivated tricks. Answer. See the Infinite Product Problem for solutions.<\/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":[32,35,152,230],"class_list":["post-915","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-calculus","tag-geometric-series","tag-power-series","tag-sequences-and-series"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/915","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=915"}],"version-history":[{"count":5,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/915\/revisions"}],"predecessor-version":[{"id":3858,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/915\/revisions\/3858"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}