Harmonic Numbers/Examples/H5
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Example of Harmonic Number
- $H_5 = \dfrac {137} {60}$
where $H_5$ denotes the fifth harmonic number.
Proof
\(\ds H_5\) | \(=\) | \(\ds \sum_{k \mathop = 1}^5 \frac 1 k\) | Definition of Harmonic Number | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 1 1 + \frac 1 2 + \frac 1 3 + \frac 1 4 + \frac 1 5\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {137} {60}\) |
$\blacksquare$