Okay, so the problem is:
$ a_n = \frac{n!}{n^n} $
And, it hints to compare this with $ \frac{1}{n} $.
I don't get really how to compare these two.. I mean, I can see that the denominator of $ a_n $ will grow much faster than the numerator. I'm guessing the limit approaches 0 as n approaches infinity, but I'm not sure how to mathematically show that $ a_n < \frac{1}{n} $
