UConn Math Club
Applications of Divergence of the Harmonic Series
Keith Conrad (University of Connecticut)
Wednesday, November 29, 2017
The harmonic series is the sum of all reciprocals 1 + 1/2 + 1/3 + 1/4 + ..., and a famous counterintuitive result from calculus (after students learn about a few convergent infinite series like the geometric series) is that the harmonic series diverges even though its general term tends to 0. This is usually the only way undergraduates see the harmonic series appear in any math classes.
Math, however, covers a lot more territory than what you see in class. The divergence of the harmonic series turns out to have applications, both to other topics in math and to events in your daily experience. By the end of the talk you will see several reasons that the divergence of the harmonic series should be completely intuitive.
Comments: Free pizza and drinks!