Question: Suppose that 0 < x1 < 1 and xn+1 = 1 - 1 - xn for n e N. Prove that xn 0 as

Suppose that 0 < x1 < 1 and xn+1 = 1 - √1 - xn for n e N. Prove that xn ↓ 0 as n → ∞ and xn+1/xn → 1/2, as n → ∞.

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