IMO 2021 Shortlist A5
Let n ě 2 be an integer, and let a1,a2,...,an be positive real numbers such that a1 a2 ¨¨¨an “1. Prove that n ÿ k“1 ak 1...
Category: Algebra
Problem
Let n ě 2 be an integer, and let a1,a2,...,an be positive real numbers such that
a1 a2 ¨¨¨an “1. Prove that n ÿ k“1 ak 1 ´ak pa1 a2 ¨¨¨ak´1q2
ă 1
.