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

• To: mathgroup at smc.vnet.net
• Subject: [mg71531] Limit of Infinitely Nested Expression (4.0 succeeds, 5.2 fails...)
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Wed, 22 Nov 2006 05:22:13 -0500 (EST)

```\$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superseded by the kernel Limit function. The package Calculus`Limit` is
obsolete.

Dimitris

```

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