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

\(\displaystyle H_2\) \(=\) \(\displaystyle \sum_{k \mathop = 1}^2 \frac 1 k\) Definition of Harmonic Number
\(\displaystyle \) \(=\) \(\displaystyle \frac 1 1 + \frac 1 2\)
\(\displaystyle \) \(=\) \(\displaystyle \dfrac 3 2\)

$\blacksquare$


Sources