$\displaystyle \lim_{n \to \infty} \displaystyle\sum_{r=1}^{n} (\frac{1}{n}) \frac{\sqrt{n+r}}{n-r}$ is equal to :

Question

( A ) $\frac{\pi + 2}{3}$
( B ) $\frac{\pi + 1}{2}$
( C ) $\frac{\pi + 2}{2}$
( D ) $\frac{\pi+2}{4}$