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 Program 
// 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;
}

Output:

e^x = 2.718282
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