What is the Integral Test for Convergence of an Infinite Series? Calculus Tests of Convergence / Divergence Integral Test for Convergence of an Infinite Series 1 Answer Wataru Oct 16, 2014 Integral Test If #f# is a function such that #f(n)=a_n#, then #sum_{n=1}^inftya_n# and #int_1^infty f(x)dx# converge or diverge together. I hope that this was helpful. Answer link Related questions How do you know when to use the integral test for an infinite series? How do you use the Integral test on the infinite series #sum_(n=1)^oo1/root5(n)# ? How do you use the Integral test on the infinite series #sum_(n=1)^oo1/n^5# ? How do you use the Integral test on the infinite series #sum_(n=1)^oo1/(2n+1)^3# ? How do you use the Integral test on the infinite series #sum_(n=1)^oo1/sqrt(n+4)# ? How do you determine if the series #ln(1/2) + ln(1/3) + ln(3/4) + ... +ln[k/(k + 1)] + ....# converges? How do you know #{-1,1,-1,1,-1,1,...}# converges or diverges? Using the integral test, how do you show whether # (1 + (1/x))^x# diverges or converges? Using the integral test, how do you show whether #sum 1/(n^2+1)# diverges or converges from n=1... How do you use the Integral Test to determine convergence or divergence of the series: #sum n... See all questions in Integral Test for Convergence of an Infinite Series Impact of this question 3700 views around the world You can reuse this answer Creative Commons License