MathDB

Turkey NMO 2017 p3

Source:

January 25, 2018

algebrainequalities

Problem Statement

Denote the sequence

a_{i,j}

in positive reals such that

a_{i,j}

a_{j,i}=1

. Let

c_i=\sum_{k=1}^{n}a_{k,i}

. Prove that

1\ge

\sum_{i=1}^{n}\dfrac {1}{c_i}