OK, maybe not a very popular kind of puzzle lol. Anyway, here's the solution:click to show
It is true that the limit of s-n is the circle.
It is also true that the limit of the length of s-n is 4.
However, what we need here is not the limit of the length of s-n, but
rather the length of the limit of s-n, and there is no reason to assume that they are the same.
So, it does matter where you take the limit.