IMO 1988 LL VIE90

Does there exist a number lpha (0 < lpha < 1) such that there is an

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IMO 1988 LL VIE90

Origin: VIE

Problem

Does there exist a number \alpha (0 < \alpha < 1) such that there is an infinite sequence {an} of positive numbers satisfying 1 + an+1 \leqan + \alpha nan, n = 1, 2, . . .?