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## Homework Statement

Is the sequence {(n!)/(n^n)} convergent or divergent. If it is convergent, find its limit.

## Homework Equations

Usually with sequences, you just take the limit and if the limit isn't infinity, it converges... That doesn't really work here. I know I'm supposed to write out the terms, but I can't figure out where to go from there.

## The Attempt at a Solution

(n!)/(n^n) = ((1)(2)(3)...(n-1)(n))/((n)(n)(n)...(n)(n))

I think I'm supposed to say that this is less than something that goes to zero, but I don't know what that something should be.

n/n = 1

Does this mean that I can cancel that out and have a list of numbers smaller than n divided by n? Then the sequence is less than 1...but I think it converges to zero, I just don't know how to show that.