# IJPAM: Volume 46, No. 3 (2008)

**SUMS OF POWERS OF INTEGERS**

Department of Mathematics

University of Sherbrooke

2500 University Boul., Sherbrooke, Quebec, J1K 2R1, CANADA

e-mail: Francois.Dubeau@usherbrooke.ca

**Abstract.**Based on a relation between ordinary and factorial powers, we present polynomial expressions for the sums of powers of integers. We extend the expressions to the sums of powers of translates of integers and the sums of powers of the terms of an arithmetic series. Recursive methods are presented to compute the coefficients, and approximations of the sums are given.

**Received: **June 3, 3008

**AMS Subject Classification: **11B83, 11B37, 41A10

**Key Words and Phrases: **ordinary and factorial powers, Eulerian number, sum of powers of integers, symmetry, polynomial, approximation

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2008

**Volume:** 46

**Issue:** 3