C Exercises: Calculate the sum of the series [ 1-X^2/2!+X^4/4!- .........]

C For Loop: Exercise-18 with Solution

Write a program in C to find the sum of the series [ 1-X^2/2!+X^4/4!- .........].

Sample Solution:

C Code:

#include <stdio.h>  // Include the standard input/output header file.

int main() {
    float x, sum, t, d;  // Declare variables to store input and intermediate values.
    int i, n;  // Declare variables for loop control and input.

    // Prompt the user to input the value of 'x'.
    printf("Input the Value of x :");
    scanf("%f", &x);  // Read the value of 'x' from the user.

    // Prompt the user to input the number of terms.
    printf("Input the number of terms : ");
    scanf("%d", &n);  // Read the value of 'n' from the user.

    sum = 1;  // Initialize 'sum' to 1, as the first term is always 1.
    t = 1;    // Initialize 't' to 1 for the first term.

    // Loop to calculate the sum of the series.
    for (i = 1; i < n; i++) {
        d = (2 * i) * (2 * i - 1);  // Calculate the denominator for the term.
        t = -t * x * x / d;        // Calculate the term value.
        sum = sum + t;             // Add the term to the sum.
    }

    // Print the final result along with the input values.
    printf("\nThe sum = %f\nNumber of terms = %d\nValue of x = %f\n", sum, n, x);

    return 0;  // Return 0 to indicate successful execution.
}

Flowchart:

or

#include <stdio.h>
int main()
{
    // Variable declaration
    float x, s, t, num = 1.00, fac = 1.00;
    int i, n, pr, y = 2, m = 1;

    // User input for x and the number of terms
    printf("Input the Value of x: ");
    scanf("%f", &x);
    printf("Input the number of terms: ");
    scanf("%d", &n);
    
    // Initializing variables for summation
    s = 1.00;
    t = 1.00;

    // Loop to calculate the sum based on the number of terms
    for (i = 1; i < n; i++)
    {
        // Loop to calculate factorial and power of x
        for (pr = 1; pr <= y; pr++)
        {
            fac = fac * pr; // Calculate factorial
            num = num * x;  // Calculate power of x
        }

        m = m * (-1);    // Alternate the sign for the power of x
        num = num * m;   // Applying the alternating sign
        t = num / fac;   // Calculate the term value for this iteration
        s = s + t;       // Add the term value to the sum
        y = y + 2;       // Increment for the next odd number (power of x)
        num = 1.00;      // Resetting num for the next iteration
        fac = 1.00;      // Resetting fac for the next iteration
    }

    // Output the result
    printf("\nThe sum = %f\nNumber of terms = %d\nValue of x = %f\n", s, n, x);

    return 0;
}

Sample Output:

Input the Value of x :2                                                                                       
Input the number of terms : 5                                                                                 
                                                                                                              
the sum = -0.415873                                                                                           
Number of terms = 5                                                                                           
value of x = 2.000000  

Flowchart:

C Programming Code Editor:

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