Telescoping method, derivative operators and harmonic number identities

TL;DR

This paper introduces a telescoping method combined with derivative operators to derive new harmonic number identities, including some previously known results, through simple binomial sums.

Contribution

It presents a novel approach that uses telescoping and derivatives to generate harmonic number identities from basic binomial sums.

Findings

Derived several new harmonic number identities.

Unified approach to known harmonic number results.

Demonstrated effectiveness of telescoping and derivatives in combinatorial identities.

Abstract

In terms of the telescoping method, a simple binomial sum is given. By applying the derivative operators to the equation just mentioned, we establish several general harmonic number identities including some known results.