$\lim_{n\to\infty} ((1+1/n)(1+2/n)...(1+n/n))^{1/n}$

Question

Hi anyone knows how to evaluate this limit?

I let $P$ = the limit

Then $\log$ both sides to bring the $1/n$ power down.

After that I integrate it by parts and gotten until

$\log P = 2\log2 - 1$

But from here how to get rid of the $\log$ and get $P$?