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Re: How to examine x=(x+a)/b

  • To: mathgroup at smc.vnet.net
  • Subject: [mg40924] Re: [mg40900] How to examine x=(x+a)/b
  • From: Bobby Treat <drmajorbob+MathGroup3528 at mailblocks.com>
  • Date: Thu, 24 Apr 2003 05:29:04 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Ponder this for various n:

Clear[a,b,x]
n = 8;
Simplify@Nest[(# + a)/b &, x, n]

Why is that the right expression, and what happens when n gets large?  
What if Abs[b] < 1?  What if b = 1?  What if b = -1?  What if Abs[b] > 
1?

Bobby

-----Original Message-----
From: Andy <news at andyhemmings.com>
To: mathgroup at smc.vnet.net
Subject: [mg40924] [mg40900] How to examine x=(x+a)/b

Hi

I have been asked to examine the following as part of some homework.

  x=(x+a)/b

I know the calculation repeats its self and reaches a point where the
input and output numbers are the same, however, i cant explain why and
how.

Any help or guidance would be appreciated.


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