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MathGroup Archive 2006

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How to explain unexpected behaviour of Fibonacci[]?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70444] How to explain unexpected behaviour of Fibonacci[]?
  • From: Peter Pein <petsie at dordos.net>
  • Date: Mon, 16 Oct 2006 02:36:00 -0400 (EDT)

Dear group,

today I came across a strange behaviour either of Limit[] or of Fibonacci[];

Limit[Log[Fibonacci[n]]/n, n -> Infinity]
--> 0
This is wrong.

NLimit[Log[Fibonacci[n]]/n, n -> Infinity]
--> 0.4812124345417209
is an approximation

and to let Mathematica do all the work:

Limit[Log[SeriesTerm[FullSimplify[
  PowerSum[Fibonacci[n], {x, n}]], {x, 0, n}]]/n, n -> Infinity]
--> Log[(1/2)*(1 + Sqrt[5])]

N[%]
0.48121182505960347

I would expect an unevaluated Limit[Log[Fibonacci[n]]/n.n->Infinity] or
Log[GoldenRatio].

Peter


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