14. approximated

topic:

Calculating π / 4 = 1 - 1/3 + 1/5 - 1/7 + ..., until the last one is less than 10-6.

 

Ideas:

Number Sequence can be expressed as 1 / (2 × i + 1), Observe that, when i is a multiple of 2, that is positive, negative otherwise. Accumulation may be achieved by circulating, after each accumulation is determined whether the condition is satisfied.

 

Code:

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

int main()
{
    double sum = 0.0, term = 0.0;
    int i = 0;

    do {
        term = 1.0 / (i * 2 + 1);
        if (i % 2 == 0) {
            sum += term;
        } else {
            sum -= term;
        }
        ++i;
    } while (term > 1e-6);

    cout << setprecision(6) << fixed << sum << endl;

    return 0;
}