algo_1

//#include "stdafx.h"
#include <iostream>
#include <math.h>

int main()
{
    double epsilon = pow(10,-6.0);

    int k = 1;

    double exact_value = pow(2, 0.5) / 2;

    std::cout << "exact value: " << exact_value << std::endl;

    double mult = 1+ (  pow(-1,1)/((2*1)+1) );

    while (  fabs(  fabs(mult) - fabs(exact_value)  )  > epsilon )
    {
        k++;
        mult *= 1+ (  pow(-1,k)/((2*k)+1)  );
    }

    std::cout << "We need to take " << k << " multipliers." << std::endl;

    return 0;

}