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Rudin Ch 3 No 16. Fix a positive number α. Choose x1 > √ α, and...

Rudin Ch 3 No 16. Fix a positive number α. Choose x1 > √ α, and define a sequence x2, x3,. . . by the recursion formula x n+1 = 1 2 (xn + α /xn ). (a) Prove that xn decreases monotonically and that lim n→∞ xn = √ α. Explain how we know xn decreases. Explain the term monotonically

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