Mathematics - Sequence & Series Question with Solution | TestHub

$\begin{array}{rl}S(x)=& (1+x)+2(1+x{)}^2+3(1+x{)}^3+..+60(1+x{)}^{60}\\ (1+x)S=& (1+x{)}^2+\dots \dots .59(1+x{)}^{60}+60(1+x{)}^{61}\\ & -xS=\frac{(1+x)(1+x{)}^{60}-1}{x}-60(1+x{)}^{61}\end{array}$
Put $\mathrm{x}=60$ $-60\mathrm{S}=\frac{61\left((61{)}^{60}-1\right)}{60}-60(61{)}^{61}$ on solving 3660