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Behavior of u_n

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September 15, 2010
functionlimitalgebraSequencerecurrence relationIMO Shortlist

Problem Statement

A sequence of real numbers u1,u2,u3,…u_1, u_2, u_3, \dots is determined by u1u_1 and the following recurrence relation for n≥1n \geq 1: 4un+1=64un+15.34u_{n+1} = \sqrt[3]{ 64u_n + 15.} Describe, with proof, the behavior of unu_n as n→∞.n \to \infty.
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