Harmonic Mean


 
 
Concept Explanation
 

Harmonic Mean

The harmonic mean of n numbers is the reciprocal of the arithmetic mean of the reciprocals of these n numbers.

The harmonic mean can be derived using the concept of arithmetic mean.

If a, b and c are in HP, b is the harmonic mean of a and c

The reciprocals of a, b and c are in AP

 frac{1}{a},; frac{1}{b} and frac{1}{c}; are;in;AP

As we know than the difference of the two consecutive numbers in an AP is the same. So

  frac{1}{a}-frac{1}{b}=frac{1}{b}-frac{1}{c}

therefore   frac{2}{b}=frac{1}{a}+frac{1}{c}

therefore    b=frac{2ac}{a+c}

Hence, the harmonic mean for two numbers is given by

b=frac{2ac}{a+c}

.... (More Text Available, Login?)
 
 
Related Videos
Language - English


Students / Parents Reviews [10]