# Harmonic series (mathematics)

In mathematics, the **harmonic series** is the divergent infinite series

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Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength. Every term of the series after the first is the harmonic mean of the neighboring terms; the phrase *harmonic mean* likewise derives from music.