Abstract

In this paper, we derive a formula for sum of powers of integers from Abel’s Summation Formula. This formula enables us to generate the formula for the sum of k^th power of integers, denoted by S_k(n), given the formulas of S₁(n), S₂(n), ..., S_k-1(n). Furthermore, we shall extend this formula to compute the sum of powers of an arithmetic progression. Moreover, we can combine the formula with the result of Bernoulli (Beardon, 1996) to derive another result which enables us to find Bernoulli Numbers recursively.

Keywords: Sum of powers, Arithmetic progression, Bernoulli numbers