Quote:
Originally Posted by Citrix
For k=3
S(0)=0
S(1)=(10)/3=1/3
S(2)=(11/3)/3=2/9
S(3)=(12/9)/3=7/27
...
Hope this helps

Yes, thanks. I obviously misread the problem.
For n > 0, S(n) clearly is
which is a partial sum of a geometric series with first term 1/k and ratio 1/k.
Closed form for S(n) already given. S(n)
1/(k+1) for any k > 1 whether integer or not.