Trouble getting loop to break

[Dick Moores]

I'm writing a demo of the infinite series

x**0/0! + x**1/1! + x**2/2! + x**3/3! + ...   = e**x   (x is non-negative)

It works OK for many x, but for many the loop doesn't break. Is there 
a way to get it to break where I want it to, i.e., when the sum 
equals the limit as closely as the precision allows?

Here's what I have:

======= series_xToN_OverFactorialN.py ==========================
#!/usr/bin/env python
#coding=utf-8
# series_xToN_OverFactorialN.py  limit is e**x   from p.63 in The 
Pleasures of Pi,e
from mpmath import mpf, e, exp, factorial
import math
import time
precision = 100
mpf.dps = precision
n = mpf(0)
x = mpf(raw_input("Enter a non-negative int or float: "))
term = 1
sum = 0
limit = e**x
k = 0
while True:
     k += 1
     term = x**n/factorial(n)
     sum += term
     print "     sum = %s k = %d" % (sum, k)
     print "exp(%s) = %s" % (x, exp(x))
     print "  e**%s = %s" % (x, e**x)
     print
     if sum >= limit:
         print "math.e**%s = %f" % (x, math.e**x)
         print "last term = %s" % term
         break
     time.sleep(0.2)
     n += 1

"""
Output for x == mpf(123.45):
sum = 
410822093109668964239148908443317876138879647013995774.2951431466270782257597573259486687336246984942 
k = 427
exp(123.45) = 
410822093109668964239148908443317876138879647013995774.2951431466270782257597573259486687336246984942
   e**123.45 = 
410822093109668964239148908443317876138879647013995774.2951431466270782257597573259486687336246984942
"""
====================================================

This is also on the web at <http://python.pastebin.com/f1a5b9e03>.

Examples of problem x's: 10, 20, 30, 40, 100, 101
Examples of OK x's: 0.2, 5, 10.1, 11, 33.3, 123.45

Thanks,

Dick Moores