{"id":17879,"date":"2016-09-18T15:21:04","date_gmt":"2016-09-18T15:21:04","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=17879"},"modified":"2016-09-18T15:21:04","modified_gmt":"2016-09-18T15:21:04","slug":"calculus-limn%e2%86%92%e2%88%9en1n","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-limn%e2%86%92%e2%88%9en1n\/","title":{"rendered":"Calculus:  lim<sub>n\u2192\u221e<\/sub>(n!)^(1\/n)"},"content":{"rendered":"<h1>The tutor discusses the limit, as n goes to infinity, of the nth root of n factorial.<\/h1>\n<p>It&#8217;s probably easy to agree that, for large n, n! > (n\/6)^n.<\/p>\n<p>lim<sub>n\u2192\u221e<\/sub> ((n\/6)^n)^(1\/n) = lim<sub>n\u2192\u221e<\/sub>n\/6 = \u221e<\/p>\n<p>Therefore,<\/p>\n<p>lim<sub>n\u2192\u221e<\/sub> (n!)^(1\/n) = \u221e, since for large n, n! > (n\/6)^n.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor discusses the limit, as n goes to infinity, of the nth root of n factorial. It&#8217;s probably easy to agree that, for large n, n! > (n\/6)^n. limn\u2192\u221e ((n\/6)^n)^(1\/n) = limn\u2192\u221en\/6 = \u221e Therefore, limn\u2192\u221e (n!)^(1\/n) = \u221e, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/calculus-limn%e2%86%92%e2%88%9en1n\/\"> <span class=\"screen-reader-text\">Calculus:  lim<sub>n\u2192\u221e<\/sub>(n!)^(1\/n)<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[234],"tags":[1894],"class_list":["post-17879","post","type-post","status-publish","format-standard","hentry","category-calculus","tag-limits"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17879","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=17879"}],"version-history":[{"count":4,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17879\/revisions"}],"predecessor-version":[{"id":17883,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/17879\/revisions\/17883"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=17879"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=17879"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=17879"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}