C program to calculate sum of series using predefined function

In C programming, calculating the sum of mathematical series is a common task. This program demonstrates how to calculate the sum of the series: 1 - n²/2! + n?/4! - n?/6! + n?/8! - n¹?/10! using the predefined pow() function from the math.h library.

Syntax

double pow(double base, double exponent);

Algorithm

The algorithm to calculate the sum of series using predefined function −

• Step 1: Read the value of n from user
• Step 2: Initialize factorial = 1, sum = 1, and loop counter
• Step 3: For each even power from 2 to 10:
  • Calculate factorial for current power
  • Use pow() to calculate n raised to current power
  • Apply alternating signs (negative for powers 2, 6, 10)
  • Add/subtract the term to/from sum
• Step 4: Display the final sum

Example

Following is the C program to calculate sum of series using the predefined pow() function −

Note: To compile this program, you may need to link the math library using -lm flag: gcc program.c -lm

#include <stdio.h>
#include <math.h>

int main() {
    int i, n = 5, num;
    long int fact = 1;
    double sum = 1.0;
    
    printf("Enter the n value: ");
    scanf("%d", &num);
    
    for(i = 1; i <= n; i++) {
        fact = fact * i;
        if(i % 2 == 0) {
            if(i == 2 || i == 6 || i == 10)
                sum += -pow(num, i) / fact;
            else
                sum += pow(num, i) / fact;
        }
    }
    
    printf("Sum is %.6f
", sum);
    return 0;
}

Output

Enter the n value: 10
Sum is 367.666656

How It Works

The program implements the series calculation by −

• Starting with sum = 1 (first term of the series)
• Computing factorial incrementally for each term
• Using pow(num, i) to calculate powers of n
• Applying alternating signs based on the position in series
• The series approximates the mathematical function cos(?n)

Key Points

• The pow() function requires the math.h header file
• Factorial is calculated iteratively to avoid repeated calculations
• The series uses only even powers (2, 4, 6, 8, 10) with alternating signs
• Using double for sum ensures better precision for floating-point calculations

Conclusion

This program efficiently calculates the sum of a mathematical series using the predefined pow() function. The approach demonstrates how to combine loops, conditionals, and math library functions to solve complex mathematical problems in C.