More on Faulhaber's theorem for sums of powers of integers

Abstract

In this note we consider the theorem established in arXiv:1912.07171 concerning the sums of powers of the first $n$ positive integers, $S_k = 1^k + 2^k + \cdots + n^k$, and show that it can be used to demonstrate the classical theorem of Faulhaber for both cases of odd and even $k$.