Tính tổng S = 

Câu hỏi: Tính tổng S = $\frac{-C_n^1}{2.3}+\frac{2C_n^2}{3.4}+\frac{3C_n^3}{4.5}+$$...+\frac{{\left(-1\right)}^{n}n{C}_n^n}{\left(n+1\right)\left(n+2\right)}$

A. $\frac{n}{\left(n+1\right)\left(n+2\right)}$

B. $\frac{-2n}{\left(n+1\right)\left(n+2\right)}$

C. $\frac{-n}{\left(n+1\right)\left(n+2\right)}$

D. $\frac{2n}{\left(n+1\right)\left(n+2\right)}$