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

If |a| `lt` 1 and |b| `lt 1` then the sum of the series 1+(1+a) b+(1+a+`a^(2))b^(2)+ (1+a+a^(2)+a^(3)) b^(3)+cdots` is

A

A) `(1)/((1-a)(1-b))`

B

B )`(1)/((1-a)(1-ab))`

C

C) `(1)/((1-b)(1-ab))`

D

D) `(1)/((1-a)(1-b)(1-ab))`

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