Tính tổng S=1-1/3C 1 n +1/5 C 2 n+-1/7Cn3+...+(-1)^n/2n+1 Cnn

A. $S=\frac{2.4.6....2n}{3.5.7...(2n+1)}$

B. $S=\frac{\left(2n\right)!}{(n+1)!}$

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

D. $S=\frac{{(-1)}^{2n+1}\left(2n\right)!}{(2n+1)!}$