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Re: fibonacci question

• To: mathgroup at smc.vnet.net
• Subject: [mg119467] Re: fibonacci question
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Sun, 5 Jun 2011 07:03:14 -0400 (EDT)
• References: <isd0r7$1m2$1@smc.vnet.net>

On 04/06/2011 11:19, olfa wrote:
> Hello Mathematica community,
>
> why FullSimplify[Fibonacci[cn] + Fibonacci[cn + 1]] is not simplified
> into Fibonacci[cn+2]?
> what mathematica function should I use to get this output?
>
> thank you very much for your help.
>
You cannot expect FullSimplify to use every mathematical fact in every 
possible way.

If are working with Fibonacci, and need this simplification, one way is 
to use a transformation rule:


Fibonacci[cn] + Fibonacci[cn + 
1]/.Fibonacci[x_]+Fibonacci[y_]:>Fibonacci[y+1]/;y==x+1

Note that this is a bit more general, in that it will also spot 
expressions like Fibonacci[cn-1] + Fibonacci[cn].

It doesn't depend on the order in which things are summed, and the sum 
can contain other terms as well:

In[635]:= Fibonacci[cn-1] + 
cn-1+Fibonacci[cn-2]/.Fibonacci[x_]+Fibonacci[y_]:>Fibonacci[y+1]/;y==x+1

Out[635]= -1 + cn + Fibonacci[cn]

David Bailey
http://www.dbaileyconsultancy.co.uk