Harmonic Numbers/Examples/H5

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

\(\ds \)

\(=\)

\(\ds \frac 1 1 + \frac 1 2 + \frac 1 3 + \frac 1 4 + \frac 1 5\)

\(\ds \)

\(=\)

\(\ds \dfrac {137} {60}\)

$\blacksquare$