Tính tổng

Câu hỏi: Tính tổng ${\mathrm{S}}_{\mathrm{n}}=1+2\mathrm{a}+3{\mathrm{a}}^2+4{\mathrm{a}}^3$$+...+\left(\mathrm{n}+1\right){\mathrm{a}}^{\mathrm{n}}$ (a$\ne$1 là số cho trước)

A. $\frac{\left(\mathrm{n}+1\right){\mathrm{a}}^{\mathrm{n}+2}-\left(\mathrm{n}+2\right){\mathrm{a}}^{\mathrm{n}+1}+1}{{\left(1-\mathrm{a}\right)}^2}$

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

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

D. $\frac{\left(\mathrm{n}+1\right){\mathrm{a}}^{\mathrm{n}+2}+\left(\mathrm{n}+2\right){\mathrm{a}}^{\mathrm{n}+1}-1}{{\left(1-\mathrm{a}\right)}^2}$