Zeno's Paradox?

Question

I know it's wrong but can someone explain why?

Answer 1

This web-link will lead you to a detailed explanation :
http://www.mathacademy.com/pr/prime/articles/zeno_tort/index.asp

Answer 2

In essense, Zeno's paradoxes fails to account for the fact that an infinite series can have a finite sum. Take, for example, Zeno's claim that you can never reach a given stationary point because you must first reach the halfway point. And before you can reach the halfway point, you must reach the one-quarter point. And so on. But each distance takes a finite time to travel, and that time is proportional to the distance. So it takes some time t to travel a given distance, and it takes t/2 to travel half the distance, and t/4 to travel one-fourth of the distance, and so on. There are infinitely many terms, but the infinite sum (t/2 + t/4 + t/8 + ...) has the finite result t, which we know through calculus. So even though you can divide this travel into infinitely many subdivisions, it still takes a finite amount of time to traverse them all, making the travel possible.