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Converging Root

Problem

Consider the iterative formula, un+1 = radicalun + 2. By investigating the behaviour it should become clear that all positive starting values converge to the limit 4.

What form must the positive integer, m, take, for the iterative formula, un+1 = radicalun + m, to converge to an integral root?

Problem ID: 160 (Mar 2004)     Difficulty: 3 Star

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