harmonic series

noun

, Mathematics.

1. a series in which the reciprocals of the terms form an arithmetic progression.
2. the divergent infinite series, 1 + 1/2 + 1/3 + 1/4 + 1/5 + . . . .

harmonic series

noun

1. maths a series whose terms are in harmonic progression, as in 1 + 1 2 + 1 3 + …
2. acoustics the series of tones with frequencies strictly related to one another and to the fundamental tone, as obtained by touching lightly the node points of a string while playing it. Its most important application is in the playing of brass instruments

harmonic series

1. A series whose terms are in harmonic progression, especially the series 1 + 1 2 + 1 3 + 1 4 + …. and so on.

Word History and Origins

Origin of harmonic series¹

First recorded in 1865–70

Example Sentences

Customizing the harmonic series gets more intriguing than this, though.

From Literature

If I had extracted all the terms containing 8 from the harmonic series, the remaining terms would also converge to a finite number, as it would if I extracted only the terms with a 7, or indeed with any single digit.

From Literature

Remove all terms including any number, and the thinned-out harmonic series is convergent.

From Literature

So, almost all terms in the harmonic series will eventually have a 666 in them.

From Literature

In 2008 Thomas Schmelzer and Robert Baillie calculated that the harmonic series without any term containing the number 314159 adds up to a little over 2.3 million.

From Literature