KEAM 2012 Math Paper

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Question : 41 of 120

Marks: +1, -0

The sum of first n terms of the series

1+(1+x)y+(1+x+x2)y2+(1+x+x2+x3)y3+...

is

(
1
1−x
)[
1−yn
1−y
−y(
1−xnyn
1−xy
)]
(
1
1−x
)[
1−yn
1−y2
−x(
1−xnyn
1−xy
)]
(
1
1−x
)[
1−yn
1−y
−x2(
1−xnyn
1−xy
)]
(
1
1−x
)[
1−yn
1−y
−2x(
1−xnyn
1−xy
)]
(
1
1−x
)[
1−yn
1−y
−x(
1−xnyn
1−xy
)]

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