For any integer n > 0, n! (n factorial) is defined as the product\[ n \times (n - 1) \times (n - 2) \times \ldots \times 2 \times 1. \]And 0! is defined to be 1.It is sometimes useful to have a closed-form definition instead; for this purpose, an approximation can be used. R.W. Gosper proposed the following approximation formula:\[n! \approx n^n e^{-n} \sqrt{ \left( 2n + \frac{1}{3} \right) \pi }\]a) Create a prompt that takes in n as input.b) Compute n! accurately and store the results in an appropriate variable.\[ n! = n \times (n - 1) \times (n - 2) \times \ldots \times 2 \times 1. \]c) Next, compute n! using the approximation formula and store the results in appropriate variables.d) The message displaying the result should look something like this:```5! equals approximately 119.970035! is 120 accurately.```e) Test the program on nonnegative integers less than 10. (A type int might not accommodate very large numbers, so feel free to store the values in an unsigned int data type). Find the difference between the two results for accurateness, then compute the percent error. Is the approximation a good representation of the actual value? Use printf to display the error.\[\text{percent error} = \frac{|\text{accurate value} - \text{approximate value}|}{\text{accurate value}} \times 100\]f) Ask the user if they’d like to repeat the program and allow for iterations on the program. **Note 1:** Use a constant macro for PI and use the value of 3.14159265.**Note 2:** Factorials grow quickly, so your compiler might not be able to store the factorial of a large number. Feel free to upgrade your variable type from a typical `int` to an `unsigned long long int`.**Note 3:** Make sure negative numbers are avoided for factorial calculations.

Answer: C Source Code: #include <stdio.h>#include <math.h>#include…

For any integer n > 0, n! (n factorial) is defined as the product n * n - 1 * n - 2 . * 2 * 1. And 0! is defined to be 1. It is sometimes useful to have a closed-form definition instead; for this purpose, an approximation can be used. R.W. Gosper proposed the following approximation formula: n! - n"e" 2n + TT 3 a) Create a prompt that takes in n as input. b) Compute n! accurately and store the results in an appropriate variable. n! = n * (n 1) * (n - 2) c) Next, compute n! using the approximation formula and store the results in appropriate variables. d) The message displaying the result should look something like this: 5! equals approximately 119.97003 5! is 120 accurately. e) Test the program on nonnegative integers less than 10. (A type int might not accommodate overly large numbers so feel free to store the values in an unsigned int data type). Find the difference between the two results for accurateness, then compute the percent error. Is the approximation a good representation of the actual value? Use printf to display the error. Jaccurate value – approximate value| percent error = x 100 accurate value f) Ask the user if they'd like to repeat the program and allow for iterations on the program.

For any integer n > 0, n! (n factorial) is defined as the product n * n - 1 * n - 2 . * 2 * 1. And 0! is defined to be 1. It is sometimes useful to have a closed-form definition instead; for this purpose, an approximation can be used. R.W. Gosper proposed the following approximation formula: n! - n"e" 2n + TT 3 a) Create a prompt that takes in n as input. b) Compute n! accurately and store the results in an appropriate variable. n! = n * (n 1) * (n - 2) c) Next, compute n! using the approximation formula and store the results in appropriate variables. d) The message displaying the result should look something like this: 5! equals approximately 119.97003 5! is 120 accurately. e) Test the program on nonnegative integers less than 10. (A type int might not accommodate overly large numbers so feel free to store the values in an unsigned int data type). Find the difference between the two results for accurateness, then compute the percent error. Is the approximation a good representation of the actual value? Use printf to display the error. Jaccurate value – approximate value| percent error = x 100 accurate value f) Ask the user if they'd like to repeat the program and allow for iterations on the program.

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

For any integer n > 0, n! (n factorial) is defined as the product

\[ n \times (n - 1) \times (n - 2) \times \ldots \times 2 \times 1. \]

And 0! is defined to be 1.

It is sometimes useful to have a closed-form definition instead; for this purpose, an approximation can be used. R.W. Gosper proposed the following approximation formula:

\[
n! \approx n^n e^{-n} \sqrt{ \left( 2n + \frac{1}{3} \right) \pi }
\]

a) Create a prompt that takes in n as input.

b) Compute n! accurately and store the results in an appropriate variable.

\[ n! = n \times (n - 1) \times (n - 2) \times \ldots \times 2 \times 1. \]

c) Next, compute n! using the approximation formula and store the results in appropriate variables.

d) The message displaying the result should look something like this:

```
5! equals approximately 119.97003
5! is 120 accurately.
```

e) Test the program on nonnegative integers less than 10. (A type int might not accommodate very large numbers, so feel free to store the values in an unsigned int data type). Find the difference between the two results for accurateness, then compute the percent error. Is the approximation a good representation of the actual value? Use printf to display the error.

\[
\text{percent error} = \frac{|\text{accurate value} - \text{approximate value}|}{\text{accurate value}} \times 100
\]

f) Ask the user if they’d like to repeat the program and allow for iterations on the program.

**Note 1:** Use a constant macro for PI and use the value of 3.14159265.

**Note 2:** Factorials grow quickly, so your compiler might not be able to store the factorial of a large number. Feel free to upgrade your variable type from a typical `int` to an `unsigned long long int`.

**Note 3:** Make sure negative numbers are avoided for factorial calculations.

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