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The sum of first n terms of the series 1...

The sum of first n terms of the series `1+(1+x)y+(1+x+x^(2))y^(2)+(1+x+x^(2)+x^(3))y^(3)+....` is

A

`((1)/(1-x))[(1-y^(n))/(1-y)-y((1-x^(n)y^(n))/(1-xy))]`

B

`((1)/(1-x))[(1-y^(n))/(1-y^(2))-x((1-x^(n)y^(n))/(1-xy))]`

C

`((1)/(1-x))[(1-y^(n))/(1-y)-x^(2)((1-x^(n)y^(n))/(1-xy))]`

D

`((1)/(1-x))[(1-y^(n))/(1-y)-x((1-x^(n)y^(n))/(1-xy))]`

Text Solution

Verified by Experts

The correct Answer is:
D
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