IMO 1982 LL FRA28

Let (u1, . . . , un) be an ordered ntuple. For each k, 1 \leqk \leqn,

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IMO 1982 LL FRA28

Origin: FRA

Problem

Let (u1, . . . , un) be an ordered ntuple. For each k, 1 \leqk \leqn, define vk = k\sqrtu1u2 \cdot \cdot \cdot uk. Prove that n  k=1 vk \leqe \cdot n  k=1 uk. (e is the base of the natural logarithm).