About Bernoulli's Numbers
Mihaly Bencze, Florentin Smarandache
TL;DR
This paper provides a straightforward proof of a classical method for summing powers of natural numbers and explores various properties of Bernoulli's numbers, contributing to the understanding of these mathematical constants.
Contribution
It introduces a simple proof of Borevich-Shafarevich's method and establishes new properties of Bernoulli's numbers.
Findings
Proof of Borevich-Shafarevich's method for sum of powers
Several new properties of Bernoulli's numbers
Enhanced understanding of Bernoulli's numbers' behavior
Abstract
In this article we present a simple proof of Borevich-Shafarevich's method to compute the sum of the first n natural numbers of the same power. We also prove several properties of Bernoulli's numbers.
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Taxonomy
TopicsHistory and Theory of Mathematics · Advanced Mathematical Identities