Harmonic Numbers/Examples/H2
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Example of Harmonic Number
- $H_2 = \dfrac 3 2$
where $H_2$ denotes the second harmonic number.
Proof
\(\ds H_2\) | \(=\) | \(\ds \sum_{k \mathop = 1}^2 \frac 1 k\) | Definition of Harmonic Number | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 1 1 + \frac 1 2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac 3 2\) |
$\blacksquare$
Sources
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.7$: Harmonic Numbers: Exercise $1$