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MathGroup Archive 2006

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Re: Limit of Infinitely Nested Expression (4.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71735] Re: Limit of Infinitely Nested Expression (4.0
  • From: bobbaillie at frii.com
  • Date: Tue, 28 Nov 2006 06:03:39 -0500 (EST)
  • References: <ek97sj$irp$1@smc.vnet.net><ekeb0h$svu$1@smc.vnet.net>

danl at wolfram.com wrote:
> For examples such as this one gets results exactly
> as indicated in the TS response: use Solve to find an exact representation
> of the fixed point for the iteration.
>
>
> Daniel Lichtblau
> Wolfram Research

Yes, you can use Solve[x == Sqrt[5 + x]] to get the exact solution to
this particular problem.

But how is the user supposed to know what equation to solve?

It is unfortunate that Mathematica is unable to give an exact solution
to the limit of expressions like:

Sqrt[10]
Sqrt[5+Sqrt[10]]
Sqrt[5+ Sqrt[5+Sqrt[10]]]
...


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