//
// Filename: series.cpp
//
// Description: This program demonstrates the evaluation of several
//              mathematical series. These include the geometric series
//              and the series representation of the sine function.
//
// ENSC 104: Digital Computer Programming
//
// Section: 1 or 2
//
// Date: xx/xx/97
//
// Name: Dr. Walsh
//

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

const int NUM_TERMS = 30;

main()
	{
	double sum=0.0;
	double x=0.0;
	int i;
	int n;

	//
	// Geometric Series: converges to 1/(1-x) where x < 1.
	//
	cout << "Enter x for geometric series: ";
	cin >> x;
	cout << "You entered x = " << x << endl;

	for( n=0; n<NUM_TERMS; n++)
		{
		sum += pow( x, n );
		if ( !(n % 5) )
			cout << "\t\tsum = " << sum << endl;
		}
	cout << "\tGeometric series sums to: " << sum << endl;
	cout << "\tConvergent value is: " << (1.0/(1.0-x)) << endl;

	//
	// Sine Series: sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...
	//
	cout << "Enter x for sine series: ";
	cin >> x;
	cout << "You entered x = " << x << endl;

	double factorial = 1;
	double term = 0.0;
	sum = x;
	for( n=3,i=1; n<NUM_TERMS; n+=2,i++ )
		{
		factorial = n*(n-1)*factorial;
		term = pow( x, n )/factorial;
		term = term*pow( -1.0, i );
		sum += term;
		if ( !(n % 5) )
			cout << "\t\tsum = " << sum << endl;
		}
	cout << "sine series sums to: " << sum << endl;
	cout << "\tsin(" << x << ") = " << sin(x) << endl;

	return 0;
	}