An Inequality

TL;DR

This paper proves a new inequality involving weighted sums of products of k-subsets of positive real numbers, using harmonic means of reciprocal sets, extending the understanding of inequalities in mathematical analysis.

Contribution

It introduces a novel inequality relating weighted sums of products of k-subsets with harmonic mean weights, expanding existing inequality frameworks.

Findings

Established a new inequality involving harmonic means and subset products.

Demonstrated the inequality holds for all positive real numbers.

Provides a mathematical proof of the inequality.

Abstract

In this paper we prove that the weighted linear combination of products of the k-subsets of an n-set of positive real numbers with weight being the harmonic mean of their reciprocal sets is less than or equal to uniformly weighted sum of products of the k-subsets with weight being the harmonic mean of the whole reciprocal set.