little exponent problem

From: Usman (game_pk_at_hotmail.com)
Date: 02/06/04 

Date: Sat, 7 Feb 2004 00:36:51 +0500

 Huy everyone ,

Well I am not a big C++ programmer , I am just a little

young kid on it tryint to learn . Actually I was given an

assignment last week by my teacher which I solved

completely but was unable to go through one question.

I did solved it but I myself wasn't satisfactory. I am sending in

the question and my program code for it. I hope some one

can guide me onto it.

Bye.

Yours forever in Digital Paradise.

uSmAn

HERE GOES THE QUESTION :

The value ex can be approximated by the sum:

        1 + x + x2/2! + x3/3! + . + xn/n!

Write a program that takes a value x as input and outputs the
above sum for n taken to be each of the values 1 to 100. To
compare the value calculated by your program and the exact value,
your program should also output ex calculated using the standard function
exp.

HERE IS MY CODE FOR IT : I was unable to store value for a factorial
                                         of 100 so I deducted my loop to 34.

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

unsigned long factorial ( unsigned long );

int main()
 {
   char ch;
   do
     {
       clrscr();
       unsigned long x,n,result=1;
       unsigned long exres;
       cout << " Enter a Number : " ;
       cin >> x ;
       cout << endl << endl;
       result = 1 + x;
       for ( n = 1; n <= 33 ; n++ )
       {
          result += ( x ^ n ) / factorial(n);
         }
       exres = exp(x);
       cout << " Your result by programming formula is : " << result ;
       cout << endl << endl ;
       cout << " The exact value of the exp. func is : " << exres;
       cout << endl ;
       cout << "\n Want to perform again ? (y/n) ";
       cin >> ch;
      }
   while ( ch != 'n' );
   return 0;
  }

unsigned long factorial( unsigned long facto )
 {
   if ( facto <= 1 )
     return 1;
   else
    return facto * factorial(facto -1);
  }