I think most people miss the point of Zeno's motion paradox.
The introduction of an infinite series is not a solution, and would actually support his impossibility argument. While Achilles moves a distance x, the tortoise moves a distance y.
The underlined word is key, implying simultaneity. It was another poster (yrs ago) who called attention to the fact that the rate of motion was constant. Thus the time to overtake the tortoise was separation/(difference in speed). Zeno was demonstrating the nonsensical results from assuming space as a continuum.