Category:Definitions/Harmonic Sequences

This category contains definitions related to Harmonic Sequences.
Related results can be found in Category:Harmonic Sequences.

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:

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

Also see

• Category:Definitions/Arithmetic Sequences
• Category:Definitions/Geometric Sequences