What you perhaps don't know about the sum 1^k+2^k+3^k+...+n^k

Abstract

The article deals with the sum S_k(n) = 1^k+2^k+3^k+...+n^k and shows how to calculate the limit S_k(n)/(n^(k+1)), where n goes to infinity.

Keywords

• power sum
• mathematical induction
• limit of a sequence