Chapter 3, Problem 3.45E

(Factorial) The factorial of a nonnegative integer n is written n ! (pronounced “n factorial”) and is defined as follows: $n!=n·\left(n-1\right)·\left(n-2\right)·\mathrm{...}·1$ (for values of n greater than or equal to 1) and $n!=1\left(forn=0\right).$

For example, $5!=5·4·3·2·1$, which is 120.

1. Write a program that reads a nonnegative integer and computes and prints its factorial.
2. Write a program that estimates the value of the mathematical constant e by using the formula:

$e=1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\mathrm{...}$

3. Write a program that computes the value of e by using the formula

$e^x=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\mathrm{...}$