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

Introduction

This article will help you write a C program to find the sum of the series 1 + 1/2! + 1/3! + … + 1/n!.
This series is known as the exponential series and is commonly used in mathematics and science, especially in approximating the value of e (Euler’s number).

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Problem Statement

Given an integer value n, calculate the sum:
1 + 1/2! + 1/3! + 1/4! + … + 1/n!

This series involves computing factorial values in the denominator and summing their reciprocals.

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C Program to Calculate the Series

#include <stdio.h>

int main() {
    int i, j, n, fact;
    float sum = 1.0;

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

    for(i = 2; i <= n; i++) {
        fact = 1;
        for(j = 1; j <= i; j++) {
            fact *= j;
        }
        sum += 1.0 / fact;
    }

    printf("Sum of the series 1 + 1/2! + ... + 1/%d! is: %.4f\n", n, sum);
    return 0;
}

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Explanation

• Input: User enters n
• Outer Loop: Runs from 2 to n to calculate each factorial
• Inner Loop: Calculates factorial of i
• Sum: Adds 1/fact to the total
• Output: The final result is shown with 4 decimal precision

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Sample Output

Enter the value of n: 5  
Sum of the series 1 + 1/2! + 1/3! + 1/4! + 1/5! is: 1.7167

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Why Use This Series

• Helps understand nested loops
• Common in mathematics and scientific computing
• Used to approximate e (Euler’s constant)
• Excellent practice problem for factorial and floating-point logic

Conclusion

This C program factorial series example is a great way to practice loop nesting and precision handling in C. It helps you understand how factorials work and how to use them in real mathematical series.