/* The constant e, which is about 2.718, may be defined by the series
       e = 1/(0!) + 1/(1!) + 1/(2!) + 1/(3!) + 1/(4!) ...
   Here n! is n factorial, which is n*(n-1)*(n-2)...(3)(2)(1) for n a 
   positive integer. 0! is defined to be 1.  

   This program computes e as the sum of the series up to the 1/(12!)
   term, which should be accurate to about 9 decimal places.  
   Factorial is implemented as a function. */


#include <iostream.h>
#include <iomanip.h>

unsigned long int factorial(int);

void main(){

  double e=0;

  for (int n = 0; n <= 12; n++)  {
    e += 1./(factorial(n));
    /* cout << "main func, n = " << n  << endl; */
  }

  cout << "e is approximately " << setiosflags(ios::fixed|ios::showpoint)
       << setprecision(9) << e << ".\n";
}

unsigned long int factorial(int n){

  /* Note that the variable n is changed in this function.  This only
     changes the copy of the variable made inside this function (since
     we are using call by value.  The n variable in the main function
     is unchanged by the action of this factorial function. */

  unsigned long int fact = 1;
 
  while (n >= 1){
    /*  cout << "factorial function, n = " << n << endl;  */
    fact *=n;
    n--;
    }
  return fact;
}