This is a practice problem for a test. The test doesn't cover the comparison test, ratio test, root test or limit comparison test. I should be able to do this using the nth-term test, p-series, integral test or other basic methods of evaluating sequences and series. With that said, I don't think the integral test can be used here as the function is not decreasing. If we take the limit of the function we get:
Which is an indeterminate form. However, if I use L'Hopital's rule I don't think I will get anywhere:
And so on. No am I starting to get desperate. I think maybe I need to rewrite this. Or I have overlooked a simpler answer. Or my answer thus far is wrong.
Can I rewrite this as:
That would mean that:
And so the series diverges.