limit comparison test.
Note that if then converges.
The proposition is as follows:
If for all and there is a such that exists and is finite, then converges.
I'm honestly not even sure what angle to come at this from, since I can't see what good knowing that limit exists does in trying to prove the convergence of some series. If someone could just give me a nudge in the right direction here I should be OK.
Thanks a lot.
Actually I just noticed, I don't think you can apply the limit comparison test, as technically isn't necessarily a positive series. The proposition says that , whereas a positive series requires that , so I think I'm back at square one.
edit: but I guess the Limit Comparison test doesn't strictly require it to be a positive series, just that ...
Can't shake the feeling that my math professor is messing with me with the " isn't necessarily a positive series!!" warning.