The limit, as n approaches infinity, of (1 + (1/n))^n = e (by e, I mean 2.71828). Use this to find the limit of the following sequence:
sn = ((n+2)/(n+1))^(n+3)
$\displaystyle \begin{aligned}\lim \left(\frac{n+2}{n+1}\right)^{n+3}&= \lim\left(\frac{n+1+1}{n+1}\right)^{n+3}\\ &= \lim\left(1+\frac{1}{n+1}\right)^{n+3}\\&=\lim\lef t(1+\frac{1}{n+1}\right)^{\left(n+1\right)\left(\f rac{n+3}{n+1}\right)}\\ &= e^{\lim\frac{n+3}{n+1}}\\&=\boxed{e}\end{aligned}$