The AMATYC Review

Spring 2006, Vol.27, No.2

The Harmonic Series Diverges Again and Again

Steven J. Kifowit and Terra A. Stamps

Steve Kifowit is an associate professor of mathematics at Prairie State College. He has a BS degree in physics and applied mathematics and an MS degree in computational mathematics, both from Northern Illinois University. E-mail: skifowit@prairiestate.edu

Terra Stamps is an associate professor of mathematics and the mathematics department chair at Prairie State College. She holds a bachelor’s degree in mathematics from the University of Montevallo and a master’s degree in pure mathematics from the University of Alabama. E-mail: tstamps@prairiestate.edu
The harmonic series is one of the most celebrated infinite series of mathematics. A quick glance at a variety of modern calculus textbooks reveals that there are two very popular proofs of the divergence of the harmonic series. In this article, the
authors survey these popular proofs along with many other proofs that are equally simple and insightful. A common thread connecting the proofs is their accessibility to first-year calculus students.