Harmonic Numbers/Examples/H3
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Example of Harmonic Number
- $H_3 = \dfrac {11} 6$
where $H_3$ denotes the third harmonic number.
Proof
| \(\ds H_3\) | \(=\) | \(\ds \sum_{k \mathop = 1}^3 \frac 1 k\) | Definition of Harmonic Number | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 1 + \frac 1 2 + \frac 1 3\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {11} 6\) |
$\blacksquare$