Harmonic constant, C++ (vc++)

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#include <iostream>
#include <cmath>

double sum2( unsigned int N )
{
    const double one = 1 ; // double avoid integer division
    double sum = 0 ;

// 1/1 + 1/2 + 1/3 + 1/4 + ... + 1/N
    // loop: i goes from 1 to N
    // in each iteration through the loop, add one/i to the sum
    for( unsigned int i = 1 ; i <= N ; ++i ) sum += one/i ;

return sum ;
}

// we can reuse the implementation of sum2
void sum1( double& sum, unsigned int N ) { sum = sum2(N) ; }

int main()
{
    unsigned int N = 0 ;
    std::cout << "enter N: " ;
    std::cin >> N ;
    std::cout << N ;

std::cout << "\n1/1 + 1/2 + ... + 1/" << N << '\n' ;

std::cout << "returned by sum2: " << sum2(N) << '\n' ;

// pass by reference
    double sum ;
    sum1( sum, N ) ;
    std::cout << "computed by sum1: " << sum << '\n' ;

// to verify that the answer is close to the the computed value
    // using the standard mathematical formula for the harmonic constant
    const double gamma = 0.5772156649 ; // Euler–Mascheroni constant
    // https://en.wikipedia.org/wiki/Harmonic_number#Calculation
    const double hn_approx = gamma + std::log(N) + 0.5/N - 1.0/(12*N*N);
    std::cout << " should be about: " << hn_approx << '\n' ;
}

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Compilation time: 1,76 sec, absolute running time: 1,59 sec, absolute service time: 3,36 sec