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Zhautykov Olympiad Sequence

Source: First Zhautykov Olympiad 2005, Problem 2

December 22, 2008
functionalgebra unsolvedalgebra

Problem Statement

Let r r be a real number such that the sequence (an)n≥1 (a_{n})_{n\geq 1} of positive real numbers satisfies the equation a_{1} \plus{} a_{2} \plus{} \cdots \plus{} a_{m \plus{} 1} \leq r a_{m} for each positive integer m m. Prove that r≥4 r \geq 4.
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