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Define a sequence (xn)n≥1 recursively by x1 = 1 and xn = 1 + 1 /(xn−1)...

Define a sequence (xn)n≥1 recursively by x1 = 1 and xn = 1 + 1 /(xn−1) for n > 0. Prove that limn→∞ xn = x exists and find its value.

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