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

  • Sen-Lin Guo

    Zhengzhou Textile Institute, Zhengzhou (Henan), China
  • Feng Qi

    Jiaozuo Institute of Technology, Jiaozuo City, Henan, China


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

Cite this article

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

DOI 10.4171/ZAA/933