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 2014-05-26 13:21:08 |