If `|a| < 1 and |b| < 1,` then the sum of the series `a(a+b)+a^2(a^2+b^2)+a^3(a^3+b^3)+.....oo` is

Options

A. `(a)/(1-a)+(ab)/(1-ab)`
B. `(a^(2))/(1-a^(2))+(ab)/(1-ab)`
C. `(b)/(1-b)+(a)/(1-a)`
D. `(b^(2))/(1-b^(2))+(ab)/(1-ab)`

Answer

B