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If |a| lt 1 and |b| lt 1 , then the sum...

If `|a| lt 1 ` and |b|` lt` 1 , then the sum of the series
`a(a+b) + a^2 (a^2 + b^2) + a^3 (a^3 + b^3) `+… upto `oo` is :

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)`

Text Solution

Verified by Experts

The correct Answer is:
B
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