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Let x=1+a+a^2+...and y=1+b+b^2+..., wher...

Let `x=1+a+a^2+...`and `y=1+b+b^2+...`, where `|a|<1`and `|b|<1`. Prove that `1+a b+a^2b^2+...=(x y)/(x+y-1)`

A

`(xy)/(x-y-1)`

B

`(xy)/(x-y+1)`

C

`(xy)/(x+y+1)`

D

`(xy)/(x+y-1)`

Text Solution

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The correct Answer is:
D
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