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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*
Department of Mathematics, University of Bayreuth, Germany
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In 1631, Johannes Faulhaber published the result that sums of the form

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

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© 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