Definition:Harmonic Numbers

Definition
The harmonic numbers are denoted $H_n$ and are defined for positive integers $n$:
 * $\displaystyle \forall n \in \Z, n \ge 0: H_n = \sum_{k \mathop = 1}^n \frac 1 k$

From the definition of vacuous summation it is clear that $H_0 = 0$.

Notation
There is no standard notation for this series.

The notation given here is as advocated by Donald E. Knuth.

Also see

 * Sum of Reciprocals is Divergent whence $H_n$ is unbounded above.