// taylors.cc

#include <iostream.h>
#include <math.h>

double S(const double x, const int N)
{
	double s=1;
	double f=1;
	double inverse=0;
	
	if (x<0) inverse=1;

	for (int i=1;i<=N;i++)
	{
		f *= fabs(x/i);
		s += f;
	};
	if (inverse) s = 1/s;
	return s;
};

int main(int argc, char* argv[])
{

	const double e=exp(1);

	int N=30;
	double x;
	double s;
	double p;

	//do {
	cout << "# This program will give you a Taylor expansion of e^x for a given number x." << endl;
	cout << "# Please enter that number and I will calculate S(x,N) = " << endl;
	cout << "# 1 + x + x^2/2! + x^3/3! + ... + x^N/n!" << endl;
	cout << "# for N up to " << N << endl;
	cin >> x;
    //cout << "Please enter N (the number of iterations you wish to perform) ";
	//cin >> N;

	//cout << e << "^" << x << "= " << (p = pow(e,x)) <<endl;
	cout << "#i\tS(x,i)\t\t|(S(x, i) - e^x)/e^x|" <<endl;
	for (int i=0;i<=N;i++)
		cout << i << "\t" << (s = S(x, i)) <<  "\t\t"<< fabs(s - pow(e,x))/pow(e,x) << endl;
	//} while (x && N);
	return 0;
}