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If 0 lt x lt 1, then (3)/(2)x^(2)+(5)/(3...

If `0 lt x lt 1`, then `(3)/(2)x^(2)+(5)/(3)x^(3)+(7)/(4)x^(4)+`..............is equal to

A

`(1+x)/(1-x)+log_(e )(1-x)`

B

`(1-x)/(1+x)+log_(e )(1-x)`

C

`x((1-x)/(1+x))+log_(e )(1-x)`

D

`x((1+x)/(1-x))+log_(e )(1-x)`

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