A simple mnemonic to compute sums of powers
General Mathematics
2022-03-29 v1
Abstract
We give a simple recursive formula to obtain the general sum of the first natural numbers to the th power. Our method allows one to obtain the general formula for the th power once one knows the general formula for the th power. The method is very simple to remember owing to an analogy with differentiation and integration. Unlike previously known methods, no knowledge of additional specific constants (such as the Bernoulli numbers) is needed. This makes it particularly suitable for applications in cases when one cannot consult external references, for example mathematics competitions.
Cite
@article{arxiv.2203.13870,
title = {A simple mnemonic to compute sums of powers},
author = {Alessandro Mariani},
journal= {arXiv preprint arXiv:2203.13870},
year = {2022}
}