Courte preuve d'une identit\'{e} comportant les nombres de Bernoulli

TL;DR

This paper presents a concise proof of a generalized identity involving Bernoulli numbers, which encompasses many known Bernoulli number identities.

Contribution

It provides a new, simplified proof of a broad class of Bernoulli number identities, extending previous results.

Findings

Unified proof for multiple Bernoulli identities

Simplification of existing proofs

Generalization of Bernoulli number relations

Abstract

In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.