# C program for Exponential Series

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 ex.

The formula used to express the ex 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 ex is calculate.
• Finally the value of ex 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.

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

## Output: 