Question

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

Answer 1

`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 `1,1/2,1/3,...,1/n`

• the reciprocals are `1,2,3,...,n`
• their mean is `1/n(1+2+3+...+n) = (n+1)/2`
• whose reciprocal is `2/(n+1)`

The required harmonic mean is `2/(n+1)`