(Factorial) The factorial of a nonnegative integer n is written n! (pronounced "n fact...

(Factorial) The factorial of a nonnegative integer n is written n! (pronounced "n factorial") and is defined as follows:

n! = n•(n − 1) • (n − 2) • ... • 1 (for values of n greater than or equal to 1)

and

n! = 1 (for n = 0).

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

a) Write a program that reads a nonnegative integer and computes and prints its factorial.

b) Write a program that estimates the value of the mathematical constant e by using the formula:

c) Write a program that computes the value of ex by using the formula