so the serie is convergent.
The integral test is as follows:Theorem: The Integral TestLet be a positive continuous function that is eventually decreasing and let .Then converges if and only if converges and diverges otherwise.So to check for convergence using the integral test, you would find its integral which, like red_dog said, is as follows:
by using integration by parts twice and then evaluating the limit.
Therefore, by the Integral Test, because the integral is convergent, so is the series.