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.
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?