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Meaning
  1. 1
    English · JMdict
    mathematics harmonic progression
  2. 2
    English · Wikipedia

    In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression. In other words, it is a sequence of the form where −a/d is not a natural number and k is a natural number. (Terms in the form can be expressed as , we can let and .) Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms. It is not possible for a harmonic progression (other than the trivial case where a = 1 and k = 0) to sum to an integer. The reason is that, necessarily, at least one denominator of the progression will be divisible by a prime number that does not divide any other denominator.

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