the first n approximations of number pi in c 2b 2b

1/* This program calculates the first n approximations of the number pi
2from the infinite series
3pi = 4 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...
4All the approximations and displayed
5*/
6
7#include <iostream>
8#include <iomanip>
9
10using namespace std;
11
12int main() {
13
14	int n{ 170000 }, index=-1;
15	double approximation{ 1 };
16
17	cout << "approximation 0: 4" << endl;
18	
19
20	for (int i = 1; i <= n; i++) {
21
22		approximation += pow(-1, i) / static_cast<double>(2 * i + 1);
23		cout << "approximation " << i << ": ";
24		cout << setprecision(9) << setw(10) << left << fixed; // do not remove fixed to see all 9 decimal places
25		cout <<  4 * approximation << endl;
26
27		if (static_cast<int>(4 * approximation * 100000) == 314159 and index == -1) {
28			cout << "The " << i << "th approximation begins with 3.14159\n";
29			index = i;
30
31			char k;
32			cout << "Press Enter to continue";
33			cin >> k;
34		}
35	}
36
37	cout << "The " << index << "th approximation begins with 3.14159\n";
38	return 0;
39}