Finding the limit of $\left(\frac{n}{n+1}\right)^n$ 
Find the limit of: $$\lim_{n\to\infty}\left(\frac{n}{n+1}\right)^n$$

I'm pretty sure it goes to zero since $(n+1)^n > n^n$ but when I input large numbers it goes to $0.36$.
Also, when factoring: $$n^{1/n}\left(\frac{1}{1+\frac1n}\right)^n$$ it looks like it goes to $1$. 
So how can I find this limit?

$$ \left(\dfrac{n}{n+1}\right)^n = \frac {1}{\left(\dfrac{n+1}{n}\right)^n}=\frac {1}{\left(1+\dfrac{1}{n}\right)^n}$$
