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

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