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Re: Limit of Infinitely Nested Expression (4.0 succeeds, 5.2 fails...)


For anyone cares  have adopted this limit for the Mathematica Guidebook

for Symbolics of M. Trott where it is used version 4.0.

Dimitris

dimitris wrote:
> $VersionNumber
> 5.2
>
> 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]
>
> $VersionNumber
> 4.0
>
> Needs["Calculus`Limit`"]
>
> Limit[Nest[Sqrt[5 + #]&, 5, n], n -> Infinity]
> (1/2)*(1 + Sqrt[21])
> N[%]
> 2.79129
>
> (*Check*)
>
> Table[N[Nest[Sqrt[5 + #1] & , 5, n], 20], {n, 2, 10}]
> {2.8569700138728056542,2.8030287215568815242,2.7933901842665806726,2.\
> 7916644111115112098,2.7913553000489764255,2.7912999301488502752,2.\
> 7912900118312411350,2.7912882351758732577,2.7912879169257823550}
>
> $VersionNumber
> 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 superseded by the kernel Limit function.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.


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