What is the formula for sum of harmonic progration ?

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Solution

If a sequence is in AP, then the sequence obtained by taking the reciprocal of every term in the sequence forms an HP, that is if a,b,c,… form an AP, then $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ ,… form an HP.

Let a,b,c form an HP. Then clearly, $\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ form an AP.

b is called the Harmonic Mean.

Problems related to HP are generally solved by converting it into an AP.
Relationship between Arithmetic, Harmonic and Geometric Mean
$A M * H M = G M^{2}$
$A M > G M > H M$

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