#!/usr/bin/env python
#------------------------------------------------------------------
#	converge.py
#
#	This program displays successive terms in the converging  
#	sequences  b = (1 + 1/n)**n  and  a = (1 + 1/n)**(n+1) .
#
#		execute using:  $ python ./converge
#
#	NOTE: This program may take several seconds to complete.
#
#	programmer: ALLAN CRUSE
#	written on: 15 FEB 2011
#------------------------------------------------------------------

num_terms = 10000

for m in range( num_terms ):
	n = m+1
	num = 1.0 + n
	den = 1.0 * n
	f = num / den
	a = f
	b = 1.0
	for k in range( n ):
		a *= f
		b *= f
	print " n=%-5u    below=%1.5f    above=%1.5f   " % (n,b,a),
	print " difference=%1.5f " % (a-b)	 	
print