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$If x = 1 + a + a^{2} + \dots . \infty, where | a | < 1 and y = 1 + b + b^{2} + \dots \infty where |b| <1, then 1 + ab$ $+ 1 + a b + a^{2} b^{2} + \dots \infty =$

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xyx+y−1

x+y−1yx

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x+y+1xy

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Correct option is A

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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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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$If x = 1 + a + a^{2} + \dots . \infty, where | a | < 1 and y = 1 + b + b^{2} + \dots \infty where |b| <1, then 1 + ab$ $+ 1 + a b + a^{2} b^{2} + \dots \infty =$