Re: Limit of Infinitely Nested Expression

*To*: mathgroup at smc.vnet.net*Subject*: [mg71446] Re: Limit of Infinitely Nested Expression*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sun, 19 Nov 2006 01:10:02 -0500 (EST)*References*: <ejmkqr$gh9$1@smc.vnet.net>

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 Infinity] (1/2)*(1 + Sqrt[21]) N[%] 2.79129 In 5.2 this package is obsolete... $VerrsionNumber 5.2 Needs["Calculus`Limit`"] Limit::obslt: Functionality previously provided by Limit.m is superseded by \ the kernel Limit function. The package Calculus`Limit` is obsolete.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.