If y = x + x2 + x3 + … ∞, where | x | < 1, then Prove that x = ( – InterviewSolution

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1.

If y = x + x2 + x3 + … ∞, where | x | < 1, then Prove that x = (y/(1 + y))

Answer»

y = x + x² + x³+ … ∞

⇒ y = x( 1 + x + x² + … ∞)

⇒ y = x (1/(1 - x))

⇒ y (1 – x) = x

⇒ y – xy – x = 0

⇒ y – x(y + 1) = 0

⇒ x(1 + y) = y

⇒ x = (y/(1 + y))

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