{"id":15282,"date":"2016-04-17T15:56:04","date_gmt":"2016-04-17T15:56:04","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=15282"},"modified":"2017-09-06T17:48:13","modified_gmt":"2017-09-06T17:48:13","slug":"math-calculus-integral-test-for-convergence","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/math-calculus-integral-test-for-convergence\/","title":{"rendered":"Math:  calculus:  integral test for convergence"},"content":{"rendered":"<h1>The tutor shows a simple example of the integral test.<\/h1>\n<p>The integral test for convergence of an infinite series states that, when a<sub>n<\/sub> = f(n) both<\/p>\n<p>\u2211a<sub>n<\/sub> and \u222b<sub>1<\/sub><sup>\u221e<\/sup>f(x)dx<\/p>\n<p>either converge or diverge.<\/p>\n<p>We can therefore use the integral test to decide whether an infinite series converges or diverges.<\/p>\n<p>Example: Does the infinite series<\/p>\n<p>\u2211<sub>1<\/sub><sup>\u221e<\/sup>(1\/x)<sup>3\/2<\/sup><\/p>\n<p>converge?<\/p>\n<p>Solution:<\/p>\n<p>Using the integral test, we have<\/p>\n<p>\u222b<sub>1<\/sub><sup>\u221e<\/sup>x<sup>-3\/2<\/sup> = -2x<sup>-1\/2<\/sup>|<sub>1<\/sub><sup>\u221e<\/sup> = 0- -2=2<\/p>\n<p>Since the integral converges, so does the series.<\/p>\n<p>HTH:)<\/p>\n<p>Source:<\/p>\n<p>Larson, Roland E. and Robert P. Hostetler. <u>Calculus<\/u>. Toronto:<br \/>\nDC Heath and Company, 1989.<\/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 shows a simple example of the integral test. The integral test for convergence of an infinite series states that, when an = f(n) both \u2211an and \u222b1\u221ef(x)dx either converge or diverge. We can therefore use the integral test &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/math-calculus-integral-test-for-convergence\/\"> <span class=\"screen-reader-text\">Math:  calculus:  integral test for convergence<\/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":[234,3],"tags":[1567],"class_list":["post-15282","post","type-post","status-publish","format-standard","hentry","category-calculus","category-math","tag-integral-test-for-convergence"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/15282","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=15282"}],"version-history":[{"count":22,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/15282\/revisions"}],"predecessor-version":[{"id":23381,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/15282\/revisions\/23381"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=15282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=15282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=15282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}