Interesting Esoterica

A simple mnemonic to compute sums of powers

Article by Alessandro Mariani
  • Published in 2022
  • Added on
We give a simple recursive formula to obtain the general sum of the first $N$ natural numbers to the $r$th power. Our method allows one to obtain the general formula for the $(r+1)$th power once one knows the general formula for the $r$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.

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key
Asimplemnemonictocomputesumsofpowers
type
article
date_added
2022-04-24
date_published
2022-09-14

BibTeX entry

@article{Asimplemnemonictocomputesumsofpowers,
	key = {Asimplemnemonictocomputesumsofpowers},
	type = {article},
	title = {A simple mnemonic to compute sums of powers},
	author = {Alessandro Mariani},
	abstract = {We give a simple recursive formula to obtain the general sum of the first {\$}N{\$}
natural numbers to the {\$}r{\$}th power. Our method allows one to obtain the general
formula for the {\$}(r+1){\$}th power once one knows the general formula for the
{\$}r{\$}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.},
	comment = {},
	date_added = {2022-04-24},
	date_published = {2022-09-14},
	urls = {http://arxiv.org/abs/2203.13870v1,http://arxiv.org/pdf/2203.13870v1},
	collections = {easily-explained,fun-maths-facts,integerology},
	url = {http://arxiv.org/abs/2203.13870v1 http://arxiv.org/pdf/2203.13870v1},
	year = 2022,
	urldate = {2022-04-24},
	archivePrefix = {arXiv},
	eprint = {2203.13870},
	primaryClass = {math.GM}
}