The Basel Problem as a Telescoping Series

Summary

The celebrated Basel Problem, that of finding the infinite sum 1 + 1/4 + 1/9 + 1/16 + …, was open for 91 years. In 1735 Euler showed that the sum is π²/6. Dozens of other solutions have been found. We give one that is short and elementary.

Additional information

Notes on contributors

David Benko

David Benko ([email protected]) received two Ph.D. degrees, from the University of South Florida and from the University of Szeged in Hungary. He is an Assistant Professor of Mathematics at the University of South Alabama. His research area is approximation theory. He will represent the AMS on the MAA Committee on the American Mathematics Competitions. His recent hobby is to use potential theory to create beautiful images and animations; see www.fractaldogs.com.