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Limit of Infinitely Nested Expression


$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.


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