11. [ARCHIMEDES] Suppose that Xo = 2V3, Yo = 3, 2Xn-lYn-l Xn = , Xn-l + Yn-l...

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11. [ARCHIMEDES] Suppose that Xo = 2V3, Yo = 3, 2Xn-lYn-l Xn = , Xn-l + Yn-l and Yn = v'XnYn-l for n E N.

(a) Prove that Xn 1 X and Yn i y, as n ---7 00, for some x, Y E R.

(b) Prove that X = Y and 3.14155 < X < 3.14161.

(The actual value of x is 7!'.)

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An Introduction To Analysis

ISBN: 9780131453333

3rd Edition

Authors: William R. Wade

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Question Posted: Jul 18, 2024 07:08 AM

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11. [ARCHIMEDES] Suppose that Xo = 2V3, Yo = 3, 2Xn-lYn-l Xn = , Xn-l + Yn-l...

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An Introduction To Analysis

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