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Question

If x<1 and y<1 then (x+y)+(x2+xy+y2)+(x3+x2y+xy2+y3)+..... is

A
x+yxy(1x)(1y)
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B
xyxy(1x)(1y)
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C
x+yxy(1+x)(1+y)
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D
xyxy(1+x)(1+y)
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Solution

The correct option is D x+yxy(1x)(1y)
The given S=(x+y)+(x2+xy+y2)+.....
=1(xy){(x2y2)+(x3y3)+(x4y4)+.....}
=1(xy){(x2+x3+....)(y2+y3+.....)}
=1(xy)(x21xy21y)=1xy(x2y2x2y+xy2(1x)(1y))=x+yxy(1x)(1y)

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