Chapter 3, Problem 24P

The natural exponential function can be expressed by $e^x={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{x^n}{n!}}$ . Determine e²by calculating the sum of the series for:

(a) n=5, (b) n=15, (c) n=25

For each part create a vector n in which the first element is 0, the increment is 1, and the last term is 5, 15, or 25. Then use element-by-element calculations to create a vector in which the elements are $\frac{x^n}{n!}$ . 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 e²calculated by MATLAB.