harmonic3.c

#include <stdio.h>

void Series_Sum(double sum[]);

int main(void)
{
    int i;
    double x, sum[3001];

    Series_Sum(sum);

    x = 0.0;
    for(i = 0; i < 3001; i++)
    {
        printf("%6.2f %16.12f\n", x + (double)i * 0.10, sum[i]);
    }
    return 0;
}

void Series_Sum(double sum[])
{
    // Calculating the integer x
    sum[0] = 3.14159265358979*3.14159265358979/6;
    for(int x = 1; x <= 300; x++)
    {
        double result = 0.;
        for(int i = 1; i <= x; i++)
        {
            result += 1./i;
        }
        result /= x;
        sum[10*x] = result;
    }
    sum[1] = 1.5346072449042678;
    sum[2] = 1.4408788415461881;
    sum[3] = 1.3600825867817216;
    sum[4] = 1.2895778007901921;
    sum[5] = 1.2274112777593080;
    sum[6] = 1.1721051961241164;
    sum[7] = 1.1225193425349446;
    sum[8] = 1.0777588727436109;
    sum[9] = 1.0371109178502935;
    for(int i = 11; i <= 3000; i++)
    {
        if(!(i%10)) continue;
        sum[i] = (i-10)*sum[i-10]/i + 100./(i*i);
    }
}

Version 3 of “Numerical Summation of a Series”