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 1)
and
$n! = 1$ (for n = 0 or n = 1)
For example, $5! = 5 · 4 · 3 · 2 · 1$, which is 120. Use while statements in each of the following:
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:
$e = 1$ + ${1}\over{1!}$ + $ {1}\over{2!}$ + $ {1}\over{3!}$ + $...$
Prompt the user for the desired accuracy of e(i.e., the number of terms in the summation).
c) Write a program that computes the value of $e^x$ by using the formula:
$e^x = 1$ + ${x}\over{1!}$ + $ {x^2}\over{2!}$ + $ {x^3}\over{3!}$ + $...$
Prompt the user for the desired accuracy of e(i.e., the number of terms in the summation)