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An illustrative derivation of the sum of fifth powers

Published online by Cambridge University Press:  24 February 2022

Michael Heinrich Baumann
Michael Heinrich Baumann*
Affiliation:
Department of Mathematics, University of Bayreuth, Germany
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In 1631, Johannes Faulhaber published the result that sums of the form

$$\sum\limits_{i = 1}^n {{i^k}} = {1^k} + {2^k} + \,...\, + {n^k}$$

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 565 , March 2022 , pp. 68 - 77
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Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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© The Authors, 2022 Published by Cambridge University Press on behalf of The Mathematical Association

References

Faulhaber, Johannes, Academia algebræ, darinnen die miraculosische Inventiones zu den höchsten Cossen weiters continuirt und profitiert werden, Augspurg (1631).Google Scholar
von Waltershausen, Wolfgang Sartorius Freiherr, Gauss zum Gedächtnis, Leipzig, S. Hirzel (1856).Google Scholar