# Definition:Harmonic Sequence

## Definition

A harmonic sequence is a sequence $\sequence {a_k}$ in $\R$ defined as:

$h_k = \dfrac 1 {a + k d}$

where:

$k \in \set {0, 1, 2, \ldots}$
$-\dfrac a d \notin \set {0, 1, 2, \ldots}$

Thus its general form is:

$\dfrac 1 a, \dfrac 1 {a + d}, \dfrac 1 {a + 2 d}, \dfrac 1 {a + 3 d}, \ldots$

### Initial Term

The term $a$ is the initial term of $\sequence {a_k}$.

### Common Difference

The term $d$ is the common difference of $\sequence {a_k}$.

## Also see

• Results about harmonic sequences can be found here.