IMO 1988 LL ICE40

A sequence of numbers an, n = 1, 2, . . ., is defined as follows:

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IMO 1988 LL ICE40

Origin: ICE

Problem

A sequence of numbers an, n = 1, 2, . . ., is defined as follows: a1 = 1/2, and for each n \geq2, an = 2n −3 2n  an−1. Prove that n k=1 ak < 1 for all n \geq1.