the first n approximations of number pi in c++ code example

Example: the first n approximations of number pi in c++

/* This program calculates the first n approximations of the number pi
from the infinite series
pi = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...
All the approximations and displayed
*/

#include 
#include 

using namespace std;

int main() {

	int n{ 170000 }, index=-1;
	double approximation{ 1 };

	cout << "approximation 0: 4" << endl;
	

	for (int i = 1; i <= n; i++) {

		approximation += pow(-1, i) / static_cast(2 * i + 1);
		cout << "approximation " << i << ": ";
		cout << setprecision(9) << setw(10) << left << fixed; // do not remove fixed to see all 9 decimal places
		cout <<  4 * approximation << endl;

		if (static_cast(4 * approximation * 100000) == 314159 and index == -1) {
			cout << "The " << i << "th approximation begins with 3.14159\n";
			index = i;

			char k;
			cout << "Press Enter to continue";
			cin >> k;
		}
	}

	cout << "The " << index << "th approximation begins with 3.14159\n";
	return 0;
}