Tính tổng S = C 0 n + (2^2 - 1)/2. (C 1 n) + (2^3 - 1)/3

Câu hỏi :

Tính tổng ${\text{S\hspace{0.17em}=\hspace{0.17em}C}}_{\text{n}}^{\text{0}}+\frac{2^2-1}{2}{\text{C}}_{\text{n}}^{\text{1}}+\frac{2^3-1}{3}{\text{C}}_{\text{n}}^2+\frac{2^4-1}{4}{\text{C}}_{\text{n}}^3+\mathrm{...}+\frac{2^{\text{n}+1}-1}{\text{n}+1}{\text{C}}_{\text{n}}^{\text{n}}$