C Program to Find the Sum of Harmonic Series 1 + 1/2 + 1/3 + … + 1/n

Introduction

In this post, we’ll learn how to write a C program to calculate the harmonic series:
1 + 1/2 + 1/3 + 1/4 + … + 1/n

The harmonic series is commonly used in mathematics, data science, and algorithm analysis. Calculating it programmatically helps reinforce loop constructs and floating-point arithmetic in C.

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Problem Statement

Given a positive integer n, compute the sum of the harmonic series up to n terms.
For example, if n = 5, the series is:
1 + 1/2 + 1/3 + 1/4 + 1/5 = 2.2833

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C Program to Find Harmonic Series Sum

#include <stdio.h>

int main() {
    int n, i;
    float sum = 0.0;

    printf("Enter the value of n: ");
    scanf("%d", &n);

    for(i = 1; i <= n; i++) {
        sum += 1.0 / i;
    }

    printf("Sum of the harmonic series up to %d terms is: %.4f\n", n, sum);

    return 0;
}

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Explanation

• Input: User enters the number n
• Loop: Runs from 1 to n and adds the reciprocal of each number to sum
• Precision: 1.0 / i ensures the division is done in float, not integer
• Output: The result is shown up to 4 decimal places using %.4f

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Example Output

Enter the value of n: 5  
Sum of the harmonic series up to 5 terms is: 2.2833

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Why This is Important

The harmonic series is widely used in:

• Time complexity of algorithms (like the Harmonic Mean)
• Network load calculations
• Theoretical mathematics and number theory
• Scientific simulations involving inverse relationships

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Conclusion

This C program harmonic series example helps beginners understand loops and floating-point calculations. It’s also a useful exercise in mathematical modeling using C programming.