IMO 1987 LL FRA14

Given n real numbers 0 < t1 \leqt2 \leq\cdot \cdot \cdot \leqtn < 1, prove that

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IMO 1987 LL FRA14

Origin: FRA

Problem

Given n real numbers 0 < t1 \leqt2 \leq\cdot \cdot \cdot \leqtn < 1, prove that (1 −t2 n)  t1 (1 −t2 1)2 + t2 (1 −t3 2)2 + \cdot \cdot \cdot + tn n (1 −tn+1 n )2  < 1.