Let g(n) = n  [n/2] + [n/3]  [n/4] + ....
Evaluate this limit:
Limit g(n)/n
n → ∞
*** [x] is the greatest integer ≤ x
As n gets larger and larger,the effect of the floor function will become less and less as the dropped fractions will be divided by ever larger n (infinitely large in the "limiting" value of n).
The result, therefore will be the same as the ordinary alternating harmonic series, that is,the natural log of 2.

Posted by Charlie
on 20140526 13:21:08 