Limit of Infinitely Nested Expression

*To*: mathgroup at smc.vnet.net*Subject*: [mg71430] Limit of Infinitely Nested Expression*From*: "dimitris" <dimmechan at yahoo.com>*Date*: Sat, 18 Nov 2006 04:41:01 -0500 (EST)

$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.