# Harmonic Numbers/Examples/H0

## Example of Harmonic Number

$H_0 = 0$

where $H_0$ denotes the zeroth harmonic number.

## Proof

 $\displaystyle H_0$ $=$ $\displaystyle \sum_{k \mathop = 1}^0 \frac 1 k$ Definition of Harmonic Number $\displaystyle$ $=$ $\displaystyle 0$ Definition of Vacuous Summation

$\blacksquare$