Let’s define partial sums of the harmonic series as follows:

,

where are positive integers. Here are a couple of facts that I didn’t know before reading *Gamma* (pages 24-25):

- is never equal to an integer.
- The only values of for which is an integer are and .

When I researching for my series of posts on conditional convergence, especially examples related to the constant , the reference *Gamma: Exploring Euler’s Constant* by Julian Havil kept popping up. Finally, I decided to splurge for the book, expecting a decent popular account of this number. After all, I’m a professional mathematician, and I took a graduate level class in analytic number theory. In short, I don’t expect to learn a whole lot when reading a popular science book other than perhaps some new pedagogical insights.

Boy, was I wrong. As I turned every page, it seemed I hit a new factoid that I had not known before.

In this series, I’d like to compile some of my favorites — while giving the book a very high recommendation.

### Like this:

Like Loading...

*Related*

*Posted by John Quintanilla on October 2, 2016*

https://meangreenmath.com/2016/10/02/what-i-learned-from-reading-gamma-exploring-eulers-constant-by-julian-havil-part-2/

## 1 Comment