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Six Ways to Sum a Series

by Dan Kalman

Award: George Pólya

Year of Award: 1994

Publication Information: The College Mathematics Journal, Vol. 24, No. 5, (1993), pp. 402-421

Summary: A discussion of the sum of squares of the recipricals of the positive integers with a review of several proofs.

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About the Author: (from The College Mathematics Journal, Vol. 24, No. 5, (1993))

Dan Kalman, “This fall I have joined the mathematics faculty at American University, Washington D.C. Prior to that I spent 8 years at the Aerospace Corporation in Los Angeles, where I worked on simulations of space systems and kept in touch with mathematics through the programs and publications of the MAA. At a national meeting I heard the presentation by Zagier referred to in the article. Convinced that this ingenious proof should be more widely known, I presented it at a meeting of the Southern California MAA section. Some enthusiastic members of the audience then shared their favorite proofs and references with me. These led to more articles and proofs, and brought me into contact with a realm of mathematics I never guessed existed. This paper was the result.”



Subject classification(s): Integers | Number Concepts | Numbers and Computation | Algebra and Number Theory | Algebra | Sequences and Series
Publication Date: 
Sunday, July 20, 2008