The value of Exponential Function e^x can be expressed using following Taylor Series.

e^x = 1 + x/1! + x^2/2! + x^3/3! + ......

*How to efficiently calculate the sum of above series?*

The series can be re-written as

e^x = 1 + (x/1) (1 + (x/2) (1 + (x/3) (........) ) )

Let the sum needs to be calculated for n terms, we can calculate sum using following loop.

for (i = n - 1, sum = 1; i > 0; --i ) sum = 1 + x * sum / i;

Following is implementation of the above idea.

## C/C++

// C Efficient program to calculate // e raise to the power x #include <stdio.h> // Returns approximate value of e^x // using sum of first n terms of Taylor Series float exponential(int n, float x) { float sum = 1.0f; // initialize sum of series for (int i = n - 1; i > 0; --i ) sum = 1 + x * sum / i; return sum; } // Driver program to test above function int main() { int n = 10; float x = 1.0f; printf("e^x = %f", exponential(n, x)); return 0; }

## Java

// Java efficient program to calculate // e raise to the power x import java.io.*; class GFG { // Function returns approximate value of e^x // using sum of first n terms of Taylor Series static float exponential(int n, float x) { // initialize sum of series float sum = 1; for (int i = n - 1; i > 0; --i ) sum = 1 + x * sum / i; return sum; } // driver program public static void main (String[] args) { int n = 10; float x = 1; System.out.println("e^x = "+exponential(n,x)); } } // Contributed by Pramod Kumar

## Python3

# Python program to calculate # e raise to the power x # Funtion to calculate value # using sum of first n terms of # Taylor Series def exponential(n, x): # initialize sum of series sum = 1.0 for i in range(n, 0, -1): sum = 1 + x * sum / i print ("e^x =", sum) # Driver program to test above function n = 10 x = 1.0 exponential(n, x) # This code is contributed by Danish Raza

## C#

// C# efficient program to calculate // e raise to the power x using System; class GFG { // Function returns approximate value of e^x // using sum of first n terms of Taylor Series static float exponential(int n, float x) { // initialize sum of series float sum = 1; for (int i = n - 1; i > 0; --i ) sum = 1 + x * sum / i; return sum; } // driver program public static void Main () { int n = 10; float x = 1; Console.Write("e^x = " + exponential(n, x)); } } // This code is contributed by nitin mittal.

## PHP

<?php // PHP Efficient program to calculate // e raise to the power x // Returns approximate value of e^x // using sum of first n terms // of Taylor Series function exponential($n, $x) { // initialize sum of series $sum = 1.0; for ($i = $n - 1; $i > 0; --$i ) $sum = 1 + $x * $sum / $i; return $sum; } // Driver Code $n = 10; $x = 1.0; echo("e^x = " . exponential($n, $x)); // This code is contributed by Ajit. ?>

Output:

e^x = 2.718282

This article is compiled by **Rahul **and reviewed by GeeksforGeeks team. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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