find the harmonic mean of the observation 1,1/2,1/3,.......,1/n
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Answer:
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
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