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Q.

If x=1+a+a2+….∞, where |a|<1 and y=1+b+b2+…∞ where b<1, then 1+ab+1+ab+a2b2+…∞=

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a

xyx+y−1

b

x+y−1yx

c

xyx+y+1

d

x+y+1xy

answer is A.

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Detailed Solution

x=11−a and y=11−b⇒a=x-1x and b=y-1y ∴1+ab+a2b2+.....∞=11-ab=xyx+y-1
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