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An Easy Sequence Problem

Source: Cono sur 1996, Problem 2

May 7, 2018
cono surSequences

Problem Statement

Consider a sequence of real numbers defined by:
an+1=an+1ana_{n + 1} = a_n + \frac{1}{a_n} for n=0,1,2,...n = 0, 1, 2, ...
Prove that, for any positive real number a0a_0, is true that a1996a_{1996} is greater than 6363.
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