Okay, I'm having a bit of trouble with this one. Neither the root test nor the ratio test is pretty. Should I try to use a different test? It's kind late, so my thoughts are a bit scrambled. I think I'm gonna try to rewrite the sum and see what that gets me.
$ \frac{n!}{n^n}=\frac{(n-1)!}{n^{n-1}}<math> Don't know what that will do, but we'll see. ~~~ $
