# 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 $$j$$ th powers" and "the sum of the first $$n$$ positive $$k$$th powers" for any $$j$$ and $$k$$.

About the Author: A.F. Beardon was at Cambridge University at the time of publication

Author (old format):
A.F. Beardon
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A.F. Beardon
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Publication Date:
Tuesday, September 23, 2008
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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 $$j$$ th powers" and "the sum of the first $$n$$ positive $$k$$th powers" for any $$j$$ and $$k$$.