Harmonic number

In mathematics the Harmonic number is given by

$H_{n}^{(m)}=\sum _{k=1}^{n}{\frac {1}{k^{m}}}$

The special case of $m=1$ is frequently written without the superscript, as

$H_{n}=\sum _{k=1}^{n}{\frac {1}{k}}$

In the limit of $n\rightarrow \infty$, the Harmonic number converges to the Riemann zeta function.

See also Harmonic Series