Tính tổng S = 1 - 1/3 C 1 n + 1/5 C 2 n - 1/7 C 3 n + ...+

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

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

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

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