Assume I have an array of $N$ (say $N$ very large) elements.
I proceed removing $1/2$ of the elements then, from what remains, I remove $1/3$ of the elements, then, from what remains, i remove $1/4$ of the elements,
and so on $1/5$, $1/6$ ...
- In how many steps, say $S(N)$, we arrive to $1$ or $0$ residual elements ?
- What is the asymptotic behavior of $S(N)$ ? Would that be essentially a logarithm or does it grow faster?