Sum of $(n+1)$ terms of the series $\large\frac{^nC_0}{2}$ - $\frac{^nC_1}{3}$ + $\frac{^nC_2}{4}$ - ...... = ?

Question

$\begin{array}{1 1} (A) \large\frac{1}{n+1} \\ (B) \large\frac{1}{n+2} \\ (C) \large\frac{1}{n(n+1)} \\ (D) \large\frac{1}{(n+1)(n+2)} \end{array}$