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

1 Answer
Jun 8, 2018

#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)#