IMO Shortlist 1975 problem 4


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2. travnja 2012.
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Let a_1, a_2, \ldots , a_n, \ldots be a sequence of real numbers such that 0 \leq a_n \leq 1 and a_n - 2a_{n+1} + a_{n+2} \geq  0 for n = 1, 2, 3, \ldots. Prove that
0 \leq (n + 1)(a_n - a_{n+1}) \leq 2 \qquad \text{ for } n = 1, 2, 3, \ldots
Izvor: Međunarodna matematička olimpijada, shortlist 1975