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A series of terms is known as a HP series when their reciprocals are in arithmetic progression(AP).  \frac{1}{AP}

So, what ever you want to calculate, (first, second, ...nth term,) calculate it in AP and make a reciprocal ( \frac{1}{AP}), to find the HP.

EXAMPLE:   \frac{1}{a}, \frac{1}{a+d}, \frac{1}{a+2d}, and so on are in HP because a, a + d, a + 2d are in AP.

  • The nth term of a HP series is [math]T_n = \frac{1}{[a+(n-1)d]}[/math]

  • In order to solve a problem on Harmonic Progression, one should make the corresponding AP series and then solve the problem.
  • nth term of H.P. = \frac{1}{(nth\ term\ of\ corresponding\ A.P.)}

  • If three terms a, b, c are in HP, then b = \frac{2ac}{a+c}.