IMO 1987 LL VIE75

Let ak be positive numbers such that a1 \geq1 and ak+1 −ak \geq1

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IMO 1987 LL VIE75

Origin: VIE

Problem

Let ak be positive numbers such that a1 \geq1 and ak+1 −ak \geq1 (k = 1, 2, . . . ). Prove that for every n \inN, n  k=1 ak+1 1987\sqrtak < 1987.