Definition:Harmonic Series

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This page is about Harmonic Series. For other uses, see Harmonic.


The series defined as:

$\ds \sum_{n \mathop = 1}^\infty \frac 1 n = 1 + \frac 1 2 + \frac 1 3 + \frac 1 4 + \cdots$

is known as the harmonic series.

General Harmonic Series

Let $\sequence {x_n}$ be a sequence of numbers such that $\sequence {\size {x_n} }$ is a harmonic sequence.

Then the series defined as:

$\ds \sum_{n \mathop = 1}^\infty x_n$

is a harmonic series.

Also see

  • Results about harmonic series (particular and general) can be found here.