#!/usr/bin/env python
#------------------------------------------------------------------
#	faster_e.py
#
#	This program shows successive partial sums from the series
#	of reciprocal-factorials (which converges quite rapidly to 
#	Euler's Number  e = 2.718... as this program illustrates). 
#
#		execute using:  $ python ./faster_e.py
#
#	programmer: ALLAN CRUSE
#	written on: 16 FEB 2011
#------------------------------------------------------------------

num_terms = 9

print
print "This program adds the reciprocals of factorials",
print "up to %u! " % num_terms
print 

factorial = 1.0
partial_sum = 1.0

for m in range( num_terms ):
	n = m+1	
	factorial *= (1.0 * n)
	reciprocal = 1.0 / factorial
	partial_sum += reciprocal
	print "\t when n=%u the sum is %1.5f " % (n,partial_sum)
print