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<iostream.h> #include<iomanip.h> #include<conio.h> void main() { int i, n; float x, sum=1, t=1; clrscr(); cout<<" Enter the value for x : "; cin>>x; cout<<" Enter the value for n : "; cin>>n; /* Loop to calculate the value of Exponential */ for(i=1;i<=n;i++) { t=t*x/i; sum=sum+t; } cout<<" The Exponential Value of "<<x<<" = "<<setprecision(4)<<sum; getch(); }

**Note: setprecision(4)** is used to **set the floating point number upto 4 decimal points.**

**iomanip.h** is a header file which contains the **setprecision() function.**

**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 **2** and ‘n’ as **5****.**

- 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<=5**) for loop condition is true

t = 1 * 2 / 1

So, **t = 2**

sum = 1 + 2

So, **sum = 3**

i++

So, **i=2**

2.2. i<=n (**2<=5)** for loop condition is true

t = 2 * 2 / 2

So, **t = 2**

sum = 3 + 2

So, **sum = 5**

i++

So, **i=3**

2.3. i<=n (**3<=5**) for loop condition is true

t = 2 * 2 / 3

So, **t = 1.3333**

sum = 5 + 1.3333

So, **sum=6.3333**

i++

So, **i=4**

2.4. i<=n (**4<=5**) for loop condition is true

t = 1.3333 * 2 / 4

So, **t = 0.6667**

sum = 6.3333 + 0.6667

So, **sum=7**

i++

So, **i=5**

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

t = 0.6667 * 2 / 5

So, **t = 0.2667**

sum = 7 + 0.2667

So, **sum=7.2667**

i++

So, **i=6**

2.6. i<=n (**6<=5**) for loop condition is false

It comes out of the for loop.

- Finally it prints
**The Exponential value of 2 = 7.2667** - Thus program execution is completed.