Hi all, I have a series sum from n = 1 to infinity for n!/n^n.
I've used the ratio test only to come up with a 1 which is obviously inconclusive. I tried the root test and also came up with a 1 though it's quite possible I mixed this up. I feel as though it has to do with either direct comparison or limit comparison but I'm drawing blanks and any help would be greatly appreciated.
For those of us who are a little slow (i.e., me), I've written out a detailed proof
We can use the ratio test to test for this series' convergence.
The ratio test specifies that if the series converges absolutely. Thus, this series converges absolutely.