IMO 2015 Shortlist A1
Suppose that a sequence a1,a2,... of positive real numbers satisfies ak1 ě kak a2 k pk ´ 1q for every positive integer k...
Category: Algebra
Problem
Suppose that a sequence a1,a2,... of positive real numbers satisfies
ak1 ě kak a2 k pk ´ 1q
for every positive integer k. Prove that a1 a2 ¨¨¨ ` an ě n for every n ě 2.
(Serbia)