MathDB
IMC 2010 Problem 1, Day 2

Source:

July 27, 2010
trigonometryreal analysisreal analysis unsolved

Problem Statement

(a)(a) A sequence x1,x2,…x_1,x_2,\dots of real numbers satisfies xn+1=xncos⁡xn for all n≥1.x_{n+1}=x_n \cos x_n \textrm{ for all } n\geq 1. Does it follows that this sequence converges for all initial values x1?x_1? (5 points)
(b)(b) A sequence y1,y2,…y_1,y_2,\dots of real numbers satisfies yn+1=ynsin⁡yn for all n≥1.y_{n+1}=y_n \sin y_n \textrm{ for all } n\geq 1. Does it follows that this sequence converges for all initial values y1?y_1? (5 points)
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