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If | x | <1 and | y | <1, the sum to infinity of the series x+

Question

If $∣ x ∣ < 1$ and $∣ y ∣ < 1$ , the sum to infinity of the series $x + y, (x^{2} + x y + y^{2}), (x^{3} + x^{2} y + x y^{2} + y^{3}), .........$ is

\frac{x + y - x y}{1 - x - y + x y}

\frac{x + y + x y}{1 - x - y + x y}

\frac{x}{1 - x} + \frac{y}{1 - y}

\frac{( x - y ) ( x + y - x y )}{1 - x - y + x y}

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Elijah Discussed

∣ x ∣ < 1

and

∣ y ∣ < 1

, the sum to infinity of the series

x + y, (x^{2} + x y + y^{2}), (x^{3} + x^{2} y + x y^{2} + y^{3}), .........

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Question Text

∣ x ∣ < 1

and

∣ y ∣ < 1

, the sum to infinity of the series

x + y, (x^{2} + x y + y^{2}), (x^{3} + x^{2} y + x y^{2} + y^{3}), .........

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