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Re: fibonacci question

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  • Subject: [mg119467] Re: fibonacci question
  • From: David Bailey <dave at>
  • Date: Sun, 5 Jun 2011 07:03:14 -0400 (EDT)
  • References: <isd0r7$1m2$>

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 + 

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] + 

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

David Bailey

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