I will try to remember how to get this!
A little later...
Rewrite this as:
Then use L'Hostpital on ln(n)/n.
Lim e^(1/n) = 1
I should just look this up, but I can't figure out how to do a search for it. It's cropped up a couple of times, but I don't recall the answer, much less how to find it.
Anyway, here it is
(I'm remembering something about taking the log of the limit perhaps?)