Introduction
In this blog, you will learn how to write a C program to evaluate the series:
sum = 1 – x + x²/2! – x³/3! + x⁴/4! – x⁵/5! + … – x⁹/9!
This series features alternating signs, increasing powers of x, and factorials in the denominators. Such series are common in scientific computing and Taylor series expansions.
Problem Statement
Create a C program to evaluate the following mathematical expression:
sum = 1 – x + x²/2! – x³/3! + x⁴/4! – x⁵/5! + … – x⁹/9!
The input is a number x provided by the user.
C Program to Evaluate the Series
#include <stdio.h>
#include <math.h>
int main() {
int i, sign = -1;
float x, sum = 1.0, term;
long factorial;
printf("Enter the value of x: ");
scanf("%f", &x);
for (i = 1; i <= 9; i++) {
factorial = 1;
for (int j = 1; j <= i; j++) {
factorial *= j;
}
term = pow(x, i) / factorial;
if (i % 2 == 0)
sum += term;
else
sum -= term;
}
printf("The value of the series is: %.4f\n", sum);
return 0;
}
Code Explanation
- User Input: Accepts the value of
x - Loop: Runs from 1 to 9
- Factorial: Calculated using an inner loop
- Term Calculation: Uses
pow(x, i)and factorial - Sign Handling: Alternates signs using
if (i % 2 == 0) - Sum: Adds or subtracts the current term from the total
Output Example
Enter the value of x: 2
The value of the series is: 0.2333
Why This Program Is Useful
- Helps understand nested loops and mathematical functions
- Demonstrates series expansion and alternating signs
- Reinforces concepts of factorials and exponents in programming
- A great exercise for mathematics and C language learners
Conclusion
This C program to evaluate series using alternating signs, powers, and factorials is a classic example of applying mathematical logic with loops. It is ideal for those learning C and aiming to understand more complex math-based programming problems.