Harmonic sequence
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In algebra, a harmonic sequence, sometimes called a harmonic progression, is a sequence of numbers such that the difference between the reciprocals of any two consecutive terms is constant. In other words, a harmonic sequence is formed by taking the reciprocals of every term in an arithmetic sequence.
For example, and
are harmonic sequences; however,
and
are not.
More formally, the sequence is a harmonic progression if and only if
A similar definition holds for infinite harmonic sequences. It appears most frequently in its three-term form: namely, that constants
,
, and
are in harmonic progression if and only if
.