# C Exercises: Calculate the sum of the series [ 1+x+x^2/2!+x^3/3!+....]

## C For Loop: Exercise-23 with Solution

Write a program in C to display the sum of the series [ 1+x+x^2/2!+x^3/3!+....].

This C program calculates and displays the sum of the series 1+x+x^2/2!+x^3/3!+…. The program prompts the user to input the value of x and the number of terms n. It then computes the sum using a loop, calculating each term by raising x to the appropriate power and dividing by the factorial of the term index. It finally adding it to the cumulative sum. The resulting sum of the series is then printed.

**Sample Solution:**

**C Code:**

```
#include <stdio.h> // Include the standard input/output header file.
void main()
{
float x, sum, no_row; // Declare variables to store input and intermediate results.
int i, n; // Declare loop control variables.
printf("Input the value of x :"); // Prompt the user for input.
scanf("%f", &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 = 1; // Initialize 'sum' to 1 as the first term in the series.
no_row = 1; // Initialize 'no_row' to 1 for the first term calculation.
for (i = 1; i < n; i++) // Loop to calculate subsequent terms in the series.
{
no_row = no_row * x / (float)i; // Calculate the next term using the given formula.
sum = sum + no_row; // Add the term to the running sum.
}
printf("\nThe sum is : %f\n", sum); // Print the final sum.
}
```

Output:

Input the value of x :3 Input number of terms : 5 The sum is : 16.375000

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