Using elementary approach and mathematical induction, several recursion formulae for S_k(n) = ∑^nₘ₌₁ m^k are presented which show that Sₖ₊₁(n) could be obtained from S_k(n) . A method and a formula of calculating Bernoulli numbers are proposed.
No takes yet. Share an insight, caveat, or question.
Feng Qi (1999) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: