The answer is clearly yes, because the numerator doesn't change as n gets big, but the denominator keeps getting more and more huge. Well we have diverged a long way from the foot race. We have proved that the sequence of times, t j , does indeed converge to a limit, and that limit is the same time that we predicted earlier, using algebra, that Achilles should be passing the tortoise. And since we know that Achilles does indeed pass the tortoise, our notion of a limit bears a true connection to reality. Zeno's dilemma was that the sequence of times leading up to the passing represented a completed infinite, yet the infinite is defined as that which never ends.
Infinites do end all the time.
And they end in a limit.