According to Zeno's paradox any object in motion must arrive at the halfway point before it can arrive at its destination. Once arriving at the halfway point, the remaining distance is once again divided in half and so on to infinity. Since it is impossible to complete this process, Zeno concluded all motion must be an illusion. Letting the length be unity, Zeno's paradox can be written in terms of the infinite sum = 1. To see how quickly this series converges to 1, compute the sum for:
(a) n = 5.
(b) n = 10.
(c) n = 40
For each part create a vector n in which the first element is 1, the increment is 1, and the last term is 5, 10, or 40. Then use element-by-element calculations to create a vector in which the elements are 1/2!. Finally, use the MATLAB built-in function sum to add the terms of the series. Compare the values obtained in parts (a), (b), and (c) with the value of 1.