IMO Shortlist 2010 problem A4


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23. lipnja 2013.
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A sequence x_1, x_2, \ldots is defined by x_1 = 1 and x_{2k}=-x_k, x_{2k-1} = (-1)^{k+1}x_k for all k \geq 1. Prove that \forall n \geq 1 x_1 + x_2 + \ldots + x_n \geq 0.

Proposed by Gerhard Wöginger, Austria
Izvor: Međunarodna matematička olimpijada, shortlist 2010