Harmonic Progression (HP):

A series of numbers is called a harmonic progression (HP) if the reciprocal of the terms are in AP. In simple terms, a, b, c, d, e, f are in HP if 1/a, 1/b, 1/c, 1/d, 1/e, 1/f are in AP.

For two terms 'a' and 'b':

Harmonic Mean = (2 a b) / (a + b)

For two numbers, if A, G, and H are respectively the arithmetic, geometric and harmonic means, then

A ≥ G ≥ H

A H = G2, i.e., A, G, H are in GP

In the below program, we will read the total number of terms from the user and print the H.P. Series and its sum on the console screen.

Program:

The source code to find the sum of the Harmonic Progression (H.P.) series is given below. The given program is compiled and executed using GCC compile on UBUNTU 18.04 OS successfully.

// C program to find the
// sum of Harmonic Progression (H.P.) series

#include <stdio.h>

int main()
{
    int n = 0;
    float i = 0;

    float sum = 0;
    float term = 0;

    printf("Enter total term: ");
    scanf("%d", &n);

    sum = 0;
    printf("1 ");
    for (i = 1; i <= n; i++) {
        printf(" + 1/%d", (int)i + 1);
        term = 1 / i;
        sum = sum + term;
    }
    printf("\nSum of H.P Series:  %f\n", sum);

    return 0;
}

Output:

RUN 1:
Enter total term: 5
1  + 1/2 + 1/3 + 1/4 + 1/5 + 1/6
Sum of H.P Series:  2.283334

RUN2:
Enter total term: 10
1  + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11
Sum of H.P Series:  2.928968

RUN 3:
Enter total term: 3
1  + 1/2 + 1/3 + 1/4
Sum of H.P Series:  1.833333

Explanation:

Here, we read the total number of terms from the user. Then we generated the H.P. series and find its total and printed them on the console screen.