Category:Harmonic Sequences

This category contains results about Harmonic Sequences.
Definitions specific to this category can be found in Definitions/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:Arithmetic Sequences
• Category:Geometric Sequences