Question

See attachment. Test for divergence.

Answer 1

Which way would be simpler? I started doing the integral test, but I wasn't having success taking the integral.

Answer 2

Yeah, that integral doesn't look nice...

For a comparison test, try comparing to the convergent series \(\displaystyle\sum\dfrac{1}{n^4}\).

You'll have to show that
\[\frac{n^2}{(2n^3+5)^2}\le\frac{1}{n^4}\]
for some sufficiently large \(n\). (What I mean by this is that the inequality may not be true for \(n=1\), but it may be for \(n\ge2\).)

Answer 3

That seems like the better way to go. Thanks.

Answer 4

Yep, you're welcome. I'll try to see if the integral is doable.

Answer 5

Don't worry about it, I discovered the correct u substitution. Thanks, though.