IMO 2007 Shortlist A6

Let a1,a2,...,a100 be nonnegative real numbers such that a2 1 +a2 2 +...+a2 100 = 1. Prove that a2 1a2 + a2 2a3 + ... + ...

imomathematicsolympiadshortlistalgebra

IMO 2007 Shortlist A6

Category: Algebra

Problem

Let a1,a2,...,a100 be nonnegative real numbers such that a2 1 +a2 2 +...+a2 100 = 1. Prove that a2 1a2 + a2 2a3 + ... + a2 100a1 < . (Poland)