Hostname: page-component-5db6c4db9b-mcx2m Total loading time: 0 Render date: 2023-03-24T03:03:46.663Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

An illustrative derivation of the sum of fifth powers

Published online by Cambridge University Press:  24 February 2022

Michael Heinrich Baumann*
Department of Mathematics, University of Bayreuth, Germany
Rights & Permissions[Opens in a new window]


HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In 1631, Johannes Faulhaber published the result that sums of the form

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

Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
© The Authors, 2022 Published by Cambridge University Press on behalf of The Mathematical Association


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