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Re: Limits of Nested Expressions

• To: mathgroup at smc.vnet.net
• Subject: [mg80732] Re: [mg80718] Limits of Nested Expressions
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 30 Aug 2007 23:39:03 -0400 (EDT)
• References: <200708300629.CAA08798@smc.twtelecom.net>

On 30 Aug 2007, at 07:29, Yaroslav Bulatov wrote:

> Is it possible to compute the following limit in Mathematica 6?
> Limit[Nest[Sqrt[5 + #]&, 5, n], n -> Infinity]
>
> It used to be possible through Calculus`Limit package, which seems to
> be gone
>
>

Fortunately this is not longer possible as it was one of the dumbest  
ideas ever implemented in Mathematica (the Calculus`Limit package did  
have a few tricks up its sleave but on the whole it was an  
embarassment for WRI and it is a very good thing that it is gone).

It is trivial to find the Limit symbolically (after proving that it  
exists):

  First[x /. Solve[Sqrt[5 + x] == x, x]]
  (1/2)*(1 + Sqrt[21])

Or numerically:

  FixedPoint[N[Sqrt[5 + #1]] & , 5]
  2.79128784747792

Andrzej Kozlowski

• References:
  • Limits of Nested Expressions
    • From: Yaroslav Bulatov <yaroslavvb@gmail.com>