How do you use the Integral test on the infinite series sum_(n=1)^oo1/root5(n)∞∑n=115√n ?

1 Answer
Wataru
Sep 17, 2014

Since the integral
int_1^oo 1/root5x dx∫∞115√xdx
diverges, we can conclude that the series
sum_{n=1}^oo 1/root5n∞∑n=115√n
also diverges by Integral Test.

Here is the details of the evaluation of the integral.

int_1^infty 1/root5x dx∫∞115√xdx

=lim_{t to infty}[5/4x^{4/5}]_1^{t}

= {5}/{4} lim_{t to infty}(t^{4/5}-1)

=5/4(infty-1)=infty

Related questions
See all questions in Integral Test for Convergence of an Infinite Series
Impact of this question
5161 views around the world
You can reuse this answer
Creative Commons License