English

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 NN natural numbers to the rrth power. Our method allows one to obtain the general formula for the (r+1)(r+1)th power once one knows the general formula for the rrth 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.

Keywords

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}
}