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