Exercise #3: Calculate the value of Pi Write a C++ program that calculates an es

Question

Exercise #3: Calculate the value of Pi Write a C++ program that calculates an estimate of the value of Pi. In mathematics, Pi is approximated by the following formula: Pi-4-4/3 + 4/5-4/7 + 4/9-4/11 +4/13 . 4/15 +4/17 The more terms you use, the closer to Pi you get (The above equation shows 9 terms). For example, if you use 5 terms to calculate Pi, your formula would be as follows: Pis 4-4/3 + 4/5-4/7 + 4/9 4-1.333333333333 + 0.8-0.571428 + 0.4444444-3.33968254. Write a program that prompts the user to enter the number of terms which will be used to calculate Pi. Also, your program should keep asking the user to re-calculate PI as long as you wish. Your program should get as close as it can to Pi- 3.141592653589793 Sample input/output: Enter number of terms for Pi calculation: 5 Your results are: Actual Calculated Pi 3.339682540 Would you like to try another Pi calculation? (y/n): Y Pi -3.141592653589793 Enter number of terms for Pi calculation: 580000 Your results are: Actual Calculated Pi -3.141590654 Would you like to try another Pi calculation? (y/n): y Pi 3.141592653589793 Enter number of terms for Pi calculation: 5ee00000 Your results are: Actual Calculated Pi -3.141592634 Would you like to try another Pi calculation? (y/n):n Pi -3.141592653589793 I am satisfied with this result. Note: Your results might be just a little different from the above as far as the precision.

Explanation / Answer

#include <iostream>

#include <cmath>

using namespace std;

int main()

{

int n ;

char ch = 'y';

double result = 0;

while(ch=='y'||ch=='Y') {

result = 0;

cout << "Enter the number of terms for PI calculations:" << endl;

cin >> n;

for(int i=0, j=1; i<n; i++, j+=2){

if(i%2 == 0)

result = result + (1/(double)j);

else

result = result - (1/(double)j);

}

result = 4 * result;

cout<<"Your results are: "<<endl;

cout<<"Actual Pi:"<<M_PI<<endl;

cout<<"Calculated Pi:"<<result<<endl;

cout<<"Would you like to try another Pi calculation? (y/n):"<<endl;

cin >> ch;

}

cout<<"I am satisifed with this result"<<endl;

return 0;

}

Output:

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