A Zeno's paradox revisited?

Consider a circle with a starting circumference of \(C_0 = 100\) units. Suppose you start on a point on that circle and proceed to walk along it until you take your first step on or past your starting position. Given the rules below:

  • each step you take is worth 1 unit;
  • for each step you take, the circumference of the circle is scaled by the formula \(C_s = C_0\times (s+1)\), where \(s\) is the number of steps made (so after the first step the circumference is now 200, after the second step the circumference is 300, etc.),

which of the following gives the best (i.e. most accurate) approximation to the number of steps needed to complete the task?

Note: If you think that the task will never be completed, then answer \(\infty\). Also, the \(\left \lfloor x \right \rfloor \) is the usual floor function.


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