This is a simple series, it was listed in the review section of my book, they state for this problem determine if the series converges or diverges by using the integral test, however, I feel limiting myself to one method of showing convergence will not help me on the test, so I need someone to check my different ways of showing this converges
The initial problem
Using the integral test
Using some simple substitution to find the integrand of
Since the limit is finite the series converges.
Using a direct comparison
We know by the p-series test for converges, thus the series converges
We can also take the limit of the series itself and apply L'Hopital's rule and see the limit is 0 but this doesn't mean much, because it could also diverge or converge