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Old inequality

Source: Kyrgyzstan TST 2009

April 14, 2009
inequalitiesinequalities proposed

Problem Statement

For any positive a1,a2,...,an a_1 ,a_2 ,...,a_n prove that \frac {{a_1 }} {{a_2 \plus{} a_3 }} \plus{} \frac {{a_2 }} {{a_3 \plus{} a_4 }} \plus{} ... \plus{} \frac {{a_n }} {{a_1 \plus{} a_2 }} > \frac {n} {4} holds.
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