Calculating Pi with C++

Given “n” by the user, this program will calculate pi based in n terms. This program ****ed me over because i thought it was asking to calculate it to n decimal places, but its really using an infinite series. So the more numbers you put it, the more accurate our estimation of pi will be.

Ex.
Inputting 10 , we get 3.232323 ( not very close )
Inputting 500, we get 3.14359 ( getting closer )
Inputting 99999, we get 3.14158 ( good enough! )


#include <iostream>
#include <cmath>
using namespace std;

int main()
{
    char run;
 do{
     //variable delcarations
     int n;
     double sum(0.0), pi;
    
     //input
     do {
        cout << "This program will calculate pi based on n terms." << endl;
        cout << "Enter number of terms to calculate pi to: " << endl;
        cin >> n;
        if (n < 0) cout << "ERROR! Invalid Input. Try again." << endl;
        else if (n == 0) cout << "That wouldnt work now, silly :-)" << endl;
     } while (n < 0 || n == 0);
    
    //processing
     for (int i = 0; i <= n; i++)
      {
        sum = sum + pow(-1, i)/(2*i+1);
      }
     
     pi = 4 * sum;
     cout << "Using " << n << " terms to calculate pi, we have exstimated pi at " << pi << endl;
     
    //run again?
     cout << "Run program again? " << endl;
     cin >> run;
     
 } while (run == 'y' || run == 'Y');
}