IMO Shortlist 2010 A4
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- Mesaje: 84
- Membru din: Dum Mar 27, 2011 10:36 pm
IMO Shortlist 2010 A4
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 $\forall n \geq 1$ $x_1 + x_2 + \ldots + x_n \geq 0.$