Harmonic Mean in HP - Practice Questions & MCQ

Harmonic Mean

If  are n positive numbers, then the Harmonic Mean of these numbers is given by  .

If a and b are two numbers and H is the HM of a and b. Then, a, H, b are in harmonic progression.  Hence,

Note that if the AM between two numbers a and b is , it does NOT follow that HM between the same numbers is . The HM is the reciprocal of 
 

Insertion of n-Harmonic Mean Between a and b

Let  be n harmonic mean between two numbers a and b. Then, is in H.P. 

Clearly, this H.P. contains n + 2 terms.

Let, D be the common difference of this A.P. Then, 

Important Property of HM

The sum of reciprocals of n harmonic means between two numbers is n times the reciprocal of a single H.M. between them.

Proof:

Let be n harmonic means between two numbers a and b. Then, is an H.P.