Choose the most appropriate options.
If `|a| lt 1 and |b| lt 1` then the sum of series
`a(a+b) +a^(2) (a^(2) +b^(2)) +a^(3) (a^(3) +b^(3)) + …` 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