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Re: Limit of Infinitely Nested Expression


What is strange is that Mathematica version 4.0 gives the right answer after
you load the package  Calculus`Limit`

$VersionNumber
4.0

Needs["Calculus`Limit`"]

Limit[Nest[Sqrt[5 + #]&, 5, n], n -> Infinity]
(1/2)*(1 + Sqrt[21])

N[%]
2.79129

In 5.2 this package is obsolete...

$VerrsionNumber
5.2
Needs["Calculus`Limit`"]
Limit::obslt: Functionality previously provided by Limit.m is
superseded by \
the kernel Limit function. The package Calculus`Limit` is obsolete.


Dimitris

dimitris wrote:
> $Version
> "5.2 for Microsoft Windows (June 20, 2005)"
>
> Why Limit fails to give answer below?
>
> Limit[Nest[Sqrt[5 + #1] & , 5, n], n -> Infinity]
> Nest::intnm : "Non - negative machine - size integer expected at
> position 3 in ` ` ".
> Limit[Nest[Sqrt[5 + #1] & , 5, n], n -> Infinity]
>
> f[n_] := N[Nest[Sqrt[5 + #1] & , 5, n], 40]
>
> ListPlot[f /@ Range[2, 20], Frame -> True, Axes -> False, PlotStyle ->
> {Blue, PointSize[0.02]}, PlotRange -> {2.7, 2.9}]
>
> Even the command
>
> Limit[f[n], n -> Infinity
>
> as well
>
> Needs["NumericalMath`NLimit`"]
> NLimit[f[n], n -> Infinity]
> 
> also fails.
> 
> Thanks in advance for any help.


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