Originally Posted by

**Dinghy** Actually I just noticed, I don't think you can apply the limit comparison test, as technically $\displaystyle \sum_{n=1}^\infty a_{n}$ isn't necessarily a positive series. The proposition says that $\displaystyle a_{n}\geq 0$, whereas a positive series requires that $\displaystyle a_{n}>0$, so I think I'm back at square one.k

edit: but I guess the Limit Comparison test doesn't strictly require it to be a positive series, just that $\displaystyle a_{n}\geq 0$...

Can't shake the feeling that my math professor is messing with me with the "$\displaystyle \sum_{n=1}^\infty a_{n}$ isn't necessarily a positive series!!" warning.