Program 46 - CSU1128 - CSE 2026 - Shoolini University

Program to generate total sum for the sequence x^1/1! + x^2/2! + x^3/3! + .....where x is entered by the user

Explanation

The program calculates the sum of the sequence \( \frac{x^1}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldots \) where \( x \) is entered by the user and the number of terms \( n \) is also specified by the user.

Header

The code begins with including the standard input-output header file using #include <stdio.h>.

Function Definitions

The program defines two functions: fact and power:

double fact(double x): Calculates the factorial of a given number \( x \).
- Initializes f to 1.
- Loops from 1 to \( x \), multiplying f by each value of i.
- Returns the factorial f.
double power(double x, double y): Calculates \( x \) raised to the power of \( y \).
- Initializes p to 1.
- Loops from 1 to \( y \), multiplying p by \( x \).
- Returns the result p.

Variable Declaration

The main() function is defined, and several variables are declared:

double x, n, s = 0, p, f, i: Variables to hold the input values, the sum, and intermediate values for power and factorial calculations.

Program Description

The program prints a description message for the user to understand its functionality.

User Input

The user is prompted to enter the values of \( x \) and \( n \):

printf("Enter the value of x and n: ");: Prompts the user to enter the values of \( x \) and \( n \).
scanf("%lf %lf", &x, &n);: Reads the values of \( x \) and \( n \) and stores them in the variables.

Sequence Sum Calculation

The program calculates the sum of the sequence:

for (i = 1; i <= n; i++): Loops through each term in the sequence.
p = power(x, i);: Calculates \( x^i \) using the power function.
f = fact(i);: Calculates \( i! \) using the fact function.
s += p / f;: Adds \( \frac{x^i}{i!} \) to the sum.

Output Result

The program prints the sum of the sequence:

printf("Sum = %.lf \n", s);: Prints the sum \( s \) formatted to one decimal place.

Program End

The program ends with return 0; to indicate successful execution.

Code

                    
/*
 * -----------------------------------------------------------
 * Logic Building with Computer Programming (CSU1128)
 * Instructor: Dr. Pankaj Vaidya | Author: Divya Mohan
 * 
 * This code is a part of the educational initiative by dmj.one
 * with aim of empowering and inspiring learners in the field of
 * Computer Science and Engineering through the respective courses.
 * 
 * (c) 2022, Divya Mohan for dmj.one. All rights reserved.
 * -----------------------------------------------------------
 */

#include <stdio.h>

double fact(double x)
{
    double f = 1, i;
    for (i = 1; i <= x; i++)
        f *= i;
    return f;
}
double power(double x, double y)
{
    double p = 1, i;
    for (i = 1; i <= y; i++)
        p *= x;
    return p;
}

int main()
{
    printf("\n\n Program to generate total sum for the sequence x^1/1! + x^2/2! + x^3/3! + .....where x is entered by the user. \n\n");

    double x, n, s = 0, p, f, i;

    printf("Enter the value of x and n: ");
    scanf("%lf %lf", &x, &n);

    for (i = 1; i <= n; i++)
    {
        p = power(x, i);
        f = fact(i);
        s += p / f;
    }
    printf("Sum = %.lf \n", s);
    return 0;
}

Output

Program to generate total sum for the sequence x^1/1! + x^2/2! + x^3/3! + .....where x is entered by the user.

Enter the value of x and n: 5 10
Sum = 145