How can Zeno's dichotomy paradox be disproved using mathematics? A brief description of the paradox taken from Wikipedia:

Suppose Sam wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.
This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility. This sequence also presents a second problem in that it contains no first distance to run, for any possible (finite) first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin.
The paradoxical conclusion then would be that travel over any finite
  distance can neither be completed nor begun, and so all motion must be
  an illusion.

How can this be disproved using math, as obviously we can all move a walk from one place to another?

If d is the distance between Sam and the bus and if Sam believes that he will never reach the bus thinking of Zeno's paradox then Sam may decide to reach 2d distance and will catch the  bus halfway to 2d.
