Suppose that x0 = 1, y0 = 0, xn = xn-1 + 2yn-1, and yn = xn-1

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Suppose that x0 = 1, y0 = 0,
xn = xn-1 + 2yn-1, and yn = xn-1 + yn-1
for n ∊ N. Prove that x2n - 2y2n = ± 1 for n ∊ N and
xn/yn → √2 as n → ∞

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 03:55 AM

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Suppose that x0 = 1, y0 = 0, xn = xn-1 + 2yn-1, and yn = xn-1

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Since x 0 1 and y 0 0 Notice that x 1 1 y 1 If y n1 n 1 and x ...View the full answer

An Introduction to Analysis

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