# What is the HM of 1,1/2,1/3.....1/n?

Jun 8, 2018

$\frac{2}{n + 1}$

#### Explanation:

To find the harmonic mean of a set of numbers, we

• take their reciprocals
• find out the mean of the reciprocals
• take the reciprocal of this mean

Now, for $1 , \frac{1}{2} , \frac{1}{3} , \ldots , \frac{1}{n}$

• the reciprocals are $1 , 2 , 3 , \ldots , n$
• their mean is $\frac{1}{n} \left(1 + 2 + 3 + \ldots + n\right) = \frac{n + 1}{2}$
• whose reciprocal is $\frac{2}{n + 1}$

The required harmonic mean is $\frac{2}{n + 1}$