find the values of p for which the series is convergent:
i'm kind of confused because i thought that the integral test was supposed to test for convergence or divergence..but don't you already know it will be convergent somewhere, because it's a p-series? i thought that you couldn't use the evaluation of the integral to tell you where the series actually converges to.. so, should i just evaluate the limit of the improper integral (once i've integrated) and then.. how do the p values i'm supposed to consider come into play?
if p=1 then i know it just comes out to be ln t...but if it's >1 or < 1 then it's the power rule... so how do you test if it's convergent? i know it's not right to just come on here and ask for answers, but i'm kind of struggling, do you think you could walk me through it?