Harmonic Numbers/Examples/H4

Example of Harmonic Number

$H_4 = \dfrac {25} {12}$

where $H_4$ denotes the fourth harmonic number.

Proof

\(\ds H_4\)

\(=\)

\(\ds \sum_{k \mathop = 1}^4 \frac 1 k\)

Definition of Harmonic Number

\(\ds \)

\(=\)

\(\ds \frac 1 1 + \frac 1 2 + \frac 1 3 + \frac 1 4\)

\(\ds \)

\(=\)

\(\ds \dfrac {25} {12}\)

$\blacksquare$