(Factorials) The factorial function is used frequently in probability problems. Using the...

(Factorials) The factorial function is used frequently in probability problems. Using the definition of factorial in Exercise, write a program that uses a for statement to evaluate the factorials of the integers from 1 to 5. Print the results in tabular format. What difficulty might prevent you from calculating the factorial of 20?

Exercise

(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 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.

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

Prompt the user for the desired accuracy of e (i.e., the number of terms in the summation).

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

Prompt the user for the desired accuracy of e (i.e., the number of terms in the summation).