S = 1*2*x0 + 2*3*x1+3*4*x2 + ......+ infinity
take integration of both side:
Sx = 1*2* $\frac{x1}{1}$ + 2*3* $\frac{x2}{2}$+3*4* $\frac{x3}{3}$ + ......+ infinity
take again integration both side:
S$\frac{x2}{2}$= x2+x3+x4+x5+.....+infinity
$\frac{S}{2}$=1+x+x2+x3+....+infinity
S=$\frac{2}{1-x}$