A simple mnemonic to compute sums of powers

• Published in 2022
• Added on 2022-04-24

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.

Links

• http://arxiv.org/abs/2203.13870v1
• http://arxiv.org/pdf/2203.13870v1

Other information

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 = {2022-12-07},
	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}
}