/* Compute the value of e using the formula 1 + 1 / 1! + 1 / 2! + 1 / 3! + 1 / 4! + ... + 1 / i! for some i > 1.  
 * As the values for both i! and 1 / i! may exceed available precision for long/double respectively, we use
 * BigInteger and BigDecimal */

import java.math.*;		// for BigInteger and BigDecimal

public class Prog10_20
{
	public static void main(String[] args)
	{
		BigDecimal e = new BigDecimal("0.0");		// our variable to store e as we compute it
		BigDecimal one = new BigDecimal("1.0");		// we need to do 1 / i!, so 1 needs to be stored in a BigDecimal for the divide operation
		BigInteger temp;							// used to store the BigInteger value of i! that we get back from getFactorial
		int x = 20;									// we are hardcoding the number of iterations here rather than inputting them
		for(int i=0;i<x;i++)						// do the main computation in this loop
		{		
			temp = getFactorial(i);					// temp = BigInteger of i!
			e = e.add(one.divide(new BigDecimal(temp), 30, BigDecimal.ROUND_UP));	// e = e + 1 / temp where e, 1 and temp are all stored in BigDecimal values
		}
		System.out.println("\nThe value of e with " + x + " iterates is computed as " + e);		// output the result
	}
	
	// given an int value i, compute i! but store it in a BigInteger just in case its too large for an int or long
	public static BigInteger getFactorial(int i)
	{
		BigInteger temp = new BigInteger("1");			// start our BigInteger at 1
		for(int j=2;j<=i;j++)							// multiply temp by 2, 3, 4, ..., i, where each value is a BigInteger * BigInteger
		{
			temp = temp.multiply(new BigInteger(""+j));	// we have to cast j as a String to be used as teh argument in the BigInteger constructor
		}
		return temp;									// return i! as a BigInteger
	}
}