New Multiple Harmonic Sum Identities

TL;DR

This paper introduces new identities involving multiple harmonic sums, derived through elementary partial fraction techniques, with applications to infinite series and congruences.

Contribution

It presents novel identities for binomial sums with harmonic numbers, expanding the mathematical toolkit for related series and congruence problems.

Findings

Proved three new identities for harmonic sum binomial series.

Applied identities to evaluate infinite series.

Established congruences related to harmonic sums.

Abstract

We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.