Harmonic Series
Definition
The harmonic series is a series formed by summing all positive unit fractions, specifically:
\[ \sum_{k=1}^{\infty} \frac{1}{k} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots\]
The divergence of the harmonic series is the classic counterexample to the converse of terms of convergent series tend to zero. See divergence of harmonic series.