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

Sen-Lin Guo; Feng Qi

doi:10.4171/zaa/933

JournalszaaVol. 18, No. 4pp. 1123–1130

Recursion Formulae for $\sum_{m = 1}^{n} m^{k}$

Sen-Lin Guo
Zhengzhou Textile Institute, Zhengzhou (Henan), China
Feng Qi
Jiaozuo Institute of Technology, Jiaozuo City, Henan, China

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Abstract

Using elementary approach and mathematical induction, several recursion formulae for $S_{k} (n) = \sum_{m = 1}^{n} m^{k}$ 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.

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Sen-Lin Guo, Feng Qi, Recursion Formulae for $\sum_{m = 1}^{n} m^{k}$ . Z. Anal. Anwend. 18 (1999), no. 4, pp. 1123–1130

DOI 10.4171/ZAA/933