The Basel Problem as a Rearrangement of Series

Author: Benko David   Molokach John  

Publisher: Mathematical Association of America

ISSN: 1931-1346

Source: The College Mathematics Journal, Vol.44, Iss.3, 2013-05, pp. : 171-176

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Abstract

We give an elementary solution to the famous Basel Problem, originally solved by Euler in 1735. We square the well-known series for arctan(1) due to Leibniz, and use a surprising relation among the re-arranged terms of this squared series.