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Vietnam NMO 2000_1

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October 26, 2008
limitalgebra unsolvedalgebra

Problem Statement

Given a real number c>0 c > 0, a sequence (xn) (x_n) of real numbers is defined by x_{n \plus{} 1} \equal{} \sqrt {c \minus{} \sqrt {c \plus{} x_n}} for n≥0 n \ge 0. Find all values of c c such that for each initial value x0 x_0 in (0,c) (0, c), the sequence (xn) (x_n) is defined for all n n and has a finite limit lim⁡xn \lim x_n when n\to \plus{} \infty.
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