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Zeitschrift für Analysis und ihre Anwendungen

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Volume 18, Issue 4, 1999, pp. 1123–1130
DOI: 10.4171/ZAA/933

Published online: 1999-12-31

Recursion Formulae for $\sum^n_{m=1} m^k$

Sen-Lin Guo[1] and Feng Qi[2]

(1) Zhengzhou Textile Institute, Zhengzhou (Henan), China
(2) Jiaozuo Institute of Technology, Jiaozuo City, Henan, China

Using elementary approach and mathematical induction, several recursion formulae for $S_k(n) = \sum^n_{m=1} m^k$ are presented which show that $S_{k+1}(n)$ could be obtained from $S_k(n)$. A method and a formula of calculating Bernoulli numbers are proposed.

Keywords: Recursion formulas, sum of powers, mathematical induction, Bernoulli numbers

Guo Sen-Lin, Qi Feng: Recursion Formulae for $\sum^n_{m=1} m^k$. Z. Anal. Anwend. 18 (1999), 1123-1130. doi: 10.4171/ZAA/933