Question

Write a C++ program that computes an approximation of pi (the mathematical constant used in many trigonometric and calculus applications) to four decimal places. A summation that can be used to compute pi is the following (from calculus). pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - ....... + (-1)ⁿ * 4/ (2n+1)Your program will compute a sequence of computations: S₀ = 4/1 S₁ = S₀ - 4/3 S₂ = S₁ + 4/5Since the above sequence So, S1, S2, ... converges to pi, we can stop when two consecutive S values differ by less than 0.00005.

Answer 1

Answer:

#include <iostream>

#include<cmath>

using namespace std;

int main()

{

double total = 0;

double check=1;

double ct=0;

double old=1;

while( fabs(total - old) > 0.00005 )

{

old=total;

total=total+check*4.0/(2.0*ct+1);

ct=ct+1;

check=0.0-check;

}

cout<<"Approximate value of pi is "<<total<<endl;

return 0;

}

Explanation:

• Initialize all the necessary variables.

• Run a while loop until the following condition is met.

fabs(total - old) > 0.00005

• Inside the while loop calculate the total value.
• Lastly, display the approximate value of pi.