1. ## limit

I have trouble finding the limit, some help please?
$\lim_{n \to \infty}\frac{(4n+2)n^n}{(n+1)^{n+1}}$

2. You need to notice that:
$\frac{{n^n }}
{{\left( {n + 1} \right)^n }} = \left( {\frac{{n + 1}}
{n}} \right)^{ - n} = \left( {1 + \frac{1}
{n}} \right)^{ - n} \to \frac{1}
{e}
$

3. $\lim_{n \to \infty} \frac{(4n+2)n^n}{(n+1)^{n+1}} = \lim_{n \to \infty} \frac{4n+2}{n+1} \frac{n^{n}}{(n+1)^{n}}$

$= \lim_{n \to \infty} \frac{4n+2}{n+1} \cdot \lim_{n \to \infty} \frac{n^{n}}{(n+1)^{n}} = \frac{4}{e}$