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...

IMO 2021 Shortlist A5

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 .