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## Homework Statement

I need to find the limit of the sequence:

[(1+1/n)(1+2/n)(1+3/n)...(1+n/n)]^(1/n) as n approaches infinity.

I know that the limit should come out to 4/e, but I cannot figure out why.

## Homework Equations

None.

## The Attempt at a Solution

The original sequence is equivalent to [(2n)!/(n!*n^n)]^(1/n), but I have absolutely no idea what to do with it after that. Can anybody point me in the right direction?