C Exercises: Calculate the sum of the series [ x - x^3 + x^5 + ......]

Last update on March 18 2025 13:35:39 (UTC/GMT +8 hours)

24. Alternate Sum Series [x - x³ + x⁵ - …] (Variant)

Write a program in C to find the sum of the series [x - x^3 + x^5 + ......].

This C program calculates the sum of the series x - x^3 + x^5 - ... up to a specified number of terms. The user inputs the value of x and the number of terms n. The program then uses a loop to compute each term of the series, alternating the sign and increasing the exponent by 2 for each subsequent term. Finally, the program sums the terms and prints the result.

Sample Solution:

C Code:

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

void main()
{
    int x, sum, ctr; // Declare variables to store input and intermediate results.

    int i, n, m, mm, nn; // Declare loop control variables and intermediate results.

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

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

    sum = x; // Initialize 'sum' to 'x' as the first term in the series.
    m = -1;  // Initialize 'm' to -1.

    printf("The values of the series: \n"); // Print a message.

    printf("%d\n", x); // Print the first term of the series.

    for (i = 1; i < n; i++) // Loop to calculate subsequent terms in the series.
    {
        ctr = (2 * i + 1); // Calculate the power of 'x' using the given formula.
        mm = pow(x, ctr); // Calculate the value of 'x' raised to the power 'ctr'.
        nn = mm * m;      // Multiply 'mm' with 'm'.
        printf("%d \n", nn); // Print the calculated term.
        sum = sum + nn;      // Add the term to the running sum.
        m = m * (-1);        // Toggle the value of 'm' between -1 and 1.
    }

    printf("\nThe sum = %d\n", sum); // Print the final sum.
}

Output:

Input the value of x :2                                                                                       
Input number of terms : 5                                                                                     
The values of the series:                                                                                     
2                                                                                                             
-8                                                                                                            
32                                                                                                            
-128                                                                                                          
512                                                                                                           
                                                                                                              
The sum = 410

Flowchart:

For more Practice: Solve these Related Problems:

Write a C program to compute the series sum for a given x and n, displaying every intermediate term.
Write a C program to calculate the series sum and determine the absolute error compared to sin(x) from math.h.
Write a C program to compute the series iteratively while checking for convergence after each term.
Write a C program to compute and then display the series terms in reverse order after summing them.

C Programming Code Editor:

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