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?

${\lim_{n\to \infty}{(\frac{n}{n+1})}^{n}}={\lim_{n\to \infty}{({1-{\frac{1}{n+1}}})}^n}=e^{\lim_{n\to \infty} \frac{-1}{n+1}*n}=e^{-1}$ where 3$^{rd}$ step is basic process for limit of form $1^{\infty}$
.So limit is $e^{-1}$
