Hi guys I've been doing some problems on series and I ran into this one,
which I have no idea how to go about doing.
Any help would be appreciated.
This justifies why the majoration will allow you to conclude.
It should be clear that since the interval of integration is positive and so is the integrand that
We can also see that it is continuous (Ill try to prove this if you need be). And finally . So we may apply the integral test
Therefore the series shares the convergence/divergence of
Now switching the order of integration gives
All of which converge (for the justification of the first just consider that . Therefore the series converges.