MathDB

another inequality wrapped in sigma and power of -1

Source: Shortlist BMO 2019, A4

November 7, 2020

Inequalityalgebrainequalitiesn-variable inequality

Problem Statement

Let

a_{ij}, i = 1, 2, \dots, m

and

j = 1, 2, \dots, n

be positive real numbers. Prove that

\sum_{i = 1}^m \left( \sum_{j = 1}^n \frac{1}{a_{ij}} \right)^{-1} \le \left( \sum_{j = 1}^n \left( \sum_{i = 1}^m a_{ij} \right)^{-1} \right)^{-1}