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
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