Here's another series I haven't been able to crack only with the comparison test (which is required because it is an exercise given before having explained the other tests regarding series). It seems to me that it converges, and it occured to me that I could use the fact that $$n^n \leq (n!)^2$$ but this hasn't helped me much.
I know Stirling's formula is inviting but I don't think it would be fair either. Sorry guys, I know I'm being pedantic.