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

• To: mathgroup at smc.vnet.net
• Subject: [mg71727] Re: Limit of Infinitely Nested Expression (4.0 succeeds, 5.2 fails...)
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Mon, 27 Nov 2006 04:05:23 -0500 (EST)
• References: <ek97sj\$irp\$1@smc.vnet.net>

```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 superseded by the kernel Limit function.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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