A power series expansion may be used to approximate the value of the exponential

Question

A power series expansion may be used to approximate the value of the exponential function e^x at some value x. The more terms are taken in the above series, the more accurate the answer becomes. Write a script which evaluates the value of e^2 (i.e., e^x w hen x = 2) by summing terms until the value of the current term is less than some value stop_va 1. When this occurs, add this term to the sum and exit the loop. Adjusting the value of stop_val will allow you to control how accurate the approximation is (i.e., how many terms are summed).

Explanation / Answer

//This function will return the approximate value of e^x using sum of first n terms of the given problem.

float exponentialcalculate(int n, float x)

{

    float sum = 1.0f; // In order to initialize the sum of the series

    for (int i = n - 1; i > 0; --i )

        sum = 1 + x * sum / i;

    return sum;

}

// This is the final driver program to test above function

int main()

{

    int n = 20;

    float x = 1.0f;

    printf("e^x = %f", exponentialcalculate(n, x));

    return 0;

}

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