MAA Writing Awards
Sums of Powers of Integers
Year of Award: 1997
Publication Information: The American Mathematical Monthly, vol. 103, 1996, pp. 201-213
Summary: This paper generalizes the well-known fact that "the sum of the first n positive cubes is the square of the sum of the first n positive numbers." The generalization examines any polynomial relationship between "the sum of the first n positive jth powers" and "the sum of the first n positive kth powers" for any j and k.
About the Author: A.F. Beardon was at Cambridge University at the time of publication