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Introduction
A series of terms is known as a HP series when the reciprocals of elements are in arithmetic progression. E.g.,1/a, 1/(a+d), 1/(a + 2d), and so on are in HP as a, a + d, a + 2d are in AP. In other words, the inverse of a harmonic sequence follows the rule of an arithmetic progression.
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Example of harmonic progression is 1/2, 1/4, 1/6, ...
If we take the reciprocal of each term of the above HP, the sequence will become 2, 4, 6, …. which is an AP with common difference of 2.
Harmonic Progression Formula: The general form of a harmonic progression:
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Harmonic Mean: If three terms a, b, c are in HP, then 1/a, 1/b and 1/c form an A.P.
Therefore, harmonic mean formula-
2/b = 1/a + 1/c
The harmonic mean b = 2ac/(a + c)
Important points: