The harmonic series is the series in which the terms are the reciprocals of the natural numbers, in order: \[\frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \dots = \sum_{n=1}^{\infty}\frac{1}{n}.\] It is not obvious what this series adds up to, or whether it adds up to anything at all. In fact, the harmonic series diverges (to \(\infty\)). There are many bare-hands ways to understand this, but we'll see it again later as part of the \(p\)-series test.