### 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`

.

- Initializes
`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`

.

- Initializes

#### 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