# 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 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 **e ^{3}**

^{ }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.**

- It assigns
**t=1**and**sum=1.** - 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.

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

## Output:

### TO DOWNLOAD THE PROGRAM CODE : CLICK HERE