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Sum

Source: Iran PPCE 2007

March 25, 2007
inequalities proposedinequalities

Problem Statement

Prove that ∑i=−20072007∣i+1∣(2)∣i∣>∑i=−20072007∣i∣(2)∣i∣\sum_{i=-2007}^{2007}\frac{\sqrt{|i+1|}}{(\sqrt2)^{|i|}}>\sum_{i=-2007}^{2007}\frac{\sqrt{|i|}}{(\sqrt2)^{|i|}}
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