IMO 1987 LL VIE76
Given two sequences of positive numbers {ak} and {bk} (k \inN)
IMO 1987 LL VIE76
Origin: VIE
Problem
Given two sequences of positive numbers {ak} and {bk} (k \inN) such that (i) ak < bk, (ii) cos akx + cos bkx \geq−1 k for all k \inN and x \inR, prove the existence of limk\to\inftyak bk and find this limit.