Thread: Sequence View Single Post
2020-03-21, 16:12   #6
Dr Sardonicus

Feb 2017
Nowhere

3,251 Posts

Quote:
 Originally Posted by Citrix For k=3 S(0)=0 S(1)=(1-0)/3=1/3 S(2)=(1-1/3)/3=2/9 S(3)=(1-2/9)/3=7/27 ... Hope this helps
Yes, thanks. I obviously misread the problem.

For n > 0, S(n) clearly is

$\sum_{i=1}^n\frac{(-1)^{i-1}}{k^i}$

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) $\rightarrow$ 1/(k+1) for any k > 1 whether integer or not.