Before going to the program for Exponential Series first let us understand what is a Exponential Series?

Exponential Series:

                Exponential Series is a series which is used to find the value of e^x.

The formula used to express the e^x as Exponential Series is

Expanding the above notation, the formula of Exponential Series is

For example,

                Let the value of x be 3.

So, the value of e³ is 20.0855

Program code for Exponential Series in C:

/* Program for Exponential Series */
#include<stdio.h>
#include<conio.h>

void main()
{
    int i, n;
    float x, sum=1, t=1;
    clrscr();
    
    printf("Enter the value for x : ");
    scanf("%f", &x);
    
    printf("\nEnter the value for n : ");
    scanf("%d", &n);
    
    /* Loop to calculate the value of Exponential */
    for(i=1;i<=n;i++)
    {
        t=t*x/i;
        sum=sum+t;
    }
    
    printf("\nThe Exponential Value of %f = %.4f", x, sum);
    getch();
}

Related: C program for Sine Series

Working:

• First the computer reads the value of  ‘x’ and ‘n’ from the user.
• Then using for loop the value of e^x is calculate.
• Finally the value of e^x is printed.

Related: C program for Cosine Series

Step by Step working of the above Program Code:

Let us assume that the user enters the value of ‘x’ as 3 and ‘n’ as 10.

1. It assigns t=1 and sum=1.
2. It assigns the value of i=1 and the loop continues till the condition of the for loop is true.

2.1.   i<=n    (1<=10)    for loop condition is true

t = 1 * 3 / 1

So,  t = 3

sum = 1 + 3

So,  sum = 4

i++

So,  i=2

2.2.   i<=n    (2<=10)    for loop condition is true

t = 3 * 3 / 2

So,  t = 4.5

sum = 4 + 4.5

So,  sum = 8.5

i++

So,  i=3

2.3.   i<=n    (3<=10)    for loop condition is true

t = 4.5 * 3 / 3

So,  t = 4.5

sum = 8.5 + 4.5

So,  sum=13

i++

So,  i=4

2.4.   i<=n    (4<=10)    for loop condition is true

t = 4.5 * 3 / 4

So,  t = 3.375

sum = 13 + 3.375

So,  sum=16.375

i++

So,  i=5

2.5.   i<=n    (5<=10)    for loop condition is true

t = 3.375 * 3 / 5

So,  t = 2.025

sum = 16.375 + 2.025

So,  sum=18.4

i++

So,  i=6

2.6.   i<=n    (6<=10)    for loop condition is true

t = 2.025 * 3 / 6

So,  t = 1.0125

sum = 18.4 + 1.0125

So,  sum=19.4125

i++

So,  i=7

2.7.   i<=n    (7<=10)    for loop condition is true

t = 1.0125 * 3 / 7

So,  t = 0.4339

sum = 19.4125 + 0.4339

So,  sum=19.8464

i++

So,  i=8

2.8.   i<=n    (8<=10)    for loop condition is true

t = 0.4339 * 3 / 8

So,  t = 0.1627

sum = 19.8464 + 0.1627

So,  sum=20.0091

i++

So,  i=9

2.9.   i<=n    (9<=10)    for loop condition is true

t = 0.1627 * 3 / 9

So,  t = 0.0542

sum = 20.0091 + 0.0542

So,  sum=20.0634

i++

So,  i=10

2.10.   i<=n    (10<=10)    for loop condition is true

t = 0.0524 * 3 / 10

So,  t = 0.01627

sum = 20.0634 + 0.01627

So,  sum=20.07966

i++

So,  i=11

2.11.  i<=n    (11<=10)    for loop condition is false

It comes out of the for loop.

3. Finally it prints The Exponential value of  3.000000 = 20.07966
4. Thus program execution is completed.

Output:

TO DOWNLOAD THE PROGRAM CODE : CLICK HERE