Question

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

Answer 1

Answer:

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