Let x=1+a+a2+…and y=1+b+b2+…, where ∣a∣<1and ∣b∣<1. Prove that 1+ab+a2b2+…=x+y−1xy

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Let {x}={1}+{a}+{a}^{{2}}+ {y}={1}+{b}+{b}^{{2}}+, where {|{a}

Question

Let $x = 1 + a + a^{2} + \dots$ and $y = 1 + b + b^{2} + \dots$ , where $∣ a ∣ < 1$ and $∣ b ∣ < 1$ . Prove that $1 + a b + a^{2} b^{2} + \dots = \frac{x y}{x + y - 1}$

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Let

x = 1 + a + a^{2} + \dots

and

y = 1 + b + b^{2} + \dots

, where

∣ a ∣ < 1

and

∣ b ∣ < 1

. Prove that

1 + a b + a^{2} b^{2} + \dots = \frac{x y}{x + y - 1}

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Question Text

Let

x = 1 + a + a^{2} + \dots

and

y = 1 + b + b^{2} + \dots

, where

∣ a ∣ < 1

and

∣ b ∣ < 1

. Prove that

1 + a b + a^{2} b^{2} + \dots = \frac{x y}{x + y - 1}