Chapter 10 Exercise 20, Introduction to Java Programming, Tenth Edition Y. Daniel LiangY.

*10.20 (Approximate e) Programming Exercise 5.26 approximates e using the following
series:

$e=1+1/1!+1/2!+1/3!+1/4!+...+1/i!$
$<br>$ $<br>$

import java.math.BigDecimal;

public class Exercise_10_20 {
 /** Main method */
 public static void main(String[] args) {
  // Displays the e value for i = 100, 200, . . . , and 1000.
  System.out.println("\n The e values for i = 100 to 1000:");
  System.out.println("-----------------------------------");
  System.out.println(" i                e");
  System.out.println("-----------------------------------");
  for (BigDecimal i = new BigDecimal("100"); 
   i.compareTo(new BigDecimal("1000")) <= 0; 
   i = i.add(new BigDecimal("100"))) {
   System.out.println(i + "    " + getE(i));
  }
 }

 /** Return e value for i */
 public static BigDecimal getE(BigDecimal v) {
  BigDecimal one = new BigDecimal("1");
  BigDecimal e = new BigDecimal("0.0");
  for (BigDecimal i = one; i.compareTo(v) <= 0; i = i.add(one)) {
   BigDecimal denominator = i;
   for (BigDecimal k = i.subtract(one); 
    k.compareTo(one) >= 1; 
    k = k.subtract(one)) {
    denominator = denominator.multiply(k);
   }
   // Use 25 digits of precision
   e = e.add(one.divide(denominator, 25, BigDecimal.ROUND_UP));  
  }
  return e;
 }
}