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Vietnam NMO 1990_1

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October 26, 2008
trigonometryalgebra unsolvedalgebra

Problem Statement

The sequence (xn) (x_n), n∈N∗ n\in\mathbb{N}^* is defined by ∣x1∣<1 |x_1|<1, and for all n≥1 n \ge 1, x_{n\plus{}1} \equal{}\frac{\minus{}x_n \plus{}\sqrt{3\minus{}3x_n^2}}{2} (a) Find the necessary and sufficient condition for x1 x_1 so that each xn>0 x_n > 0. (b) Is this sequence periodic? And why?
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