A Short Proof of a Known Relation for Consecutive Power Sums

TL;DR

This paper presents a concise proof of a well-known relation involving sums of powers of consecutive integers, simplifying the understanding of this mathematical property.

Contribution

It introduces a new, shorter proof of a classical relation between consecutive power sums, enhancing clarity and elegance in mathematical demonstration.

Findings

The proof confirms the relation's validity for all positive integers.

The method simplifies previous proofs, making the relation more accessible.

The approach may inspire similar simplifications in related mathematical proofs.

Abstract

We give a new short proof of the most simple relation between consecutive power sums of the first m positive integers.