On Monday, November 1, 2010, Professor James Sellers delivered the Fourth Annual Pi Mu Epsilon Lecture - *Revisiting What Euler and the Bernoullis Knew About Convergent Infinite Series*.

## Revisiting What Euler and the Bernoullis Knew About Convergent Infinite Series

### Abstract

All too often in first-year calculus classes, conversations about infinite series stop with discussions about convergence or divergence. Such interactions are, unfortunately, not often illuminating or intriguing. Interestingly enough, Jacob and Johann Bernoulli and Leonhard Euler (and their contemporaries in the early 18th century) knew quite a bit about how to find the ***exact*** values of numerous families of convergent infinite series. In this talk, I will show you two sets of ***exact*** results in this vein. The talk will be accessible to anyone interested in mathematics, so bring a friend!

### About the Speaker

James Sellers completed his undergraduate degree at the University of Texas at San Antonio (his hometown). He went on to receive his PhD at Penn State University, in 1992, under the direction of David Bressoud. There he learned a great deal about integer partitions and enumerative combinatorics. Upon graduation, James took a teaching position at Cedarville University in Ohio, a small, private Christian institution. At Cedarville, he taught numerous undergraduate courses (from mathematics for liberal arts majors to the standard precalculus, calculus, differential equations courses as well as upper-level courses in number theory and combinatorics). He was also heavily involved in completing undergraduate research with many students at Cedarville. In 2001, James returned to Penn State University to serve as a professor and the Associate Head for Undergraduate Mathematics where he oversees the full operations of the undergraduate mathematics endeavor. James has also been privileged to serve as a Visiting Fellow at the Isaac Newton Institute at Cambridge University (in 2008). He currently serves as the governor of the Allegheny Mountain Section of the MAA. James enjoys spending time with his wife, Mary, also an alumnus of Penn State, as well as their five children. In his "spare time", he enjoys a variety of sports, serving as webmaster of various organizations, teaching in his local church and thinking about mathematics! He is always up for a new problem!

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