S = 1 + (1+a)x + (1+a+a^2)x^2 + (1+a+a^2+a^3)x^3..............1

xS = x + (1+a)x^2 + (1+a+a^2)x^3 + ...................................2

subtract 2 from 1

S(1-x) = 1 + ax + (ax)^2 + (ax)^3 ..............................

= > S(1-x) = 1/1-ax ...........................[ summation of infinite GP with ratio =ax]

=> S = 1/(1-ax)(1-x)

 

do rate me !!