Re: Re: Limit of Infinitely Nested Expression (4.0

• To: mathgroup at smc.vnet.net
• Subject: [mg71775] Re: [mg71735] Re: Limit of Infinitely Nested Expression (4.0
• From: "Andrzej Kozlowski" <akozlowski at gmail.com>
• Date: Wed, 29 Nov 2006 02:56:04 -0500 (EST)

```The user should learn some (fairly elementary) mathematics.
The limit of a nested expression of the form: Nest[f,...], if it
exists, is a fixed point of the function f. A fixed point of f is a
root of f[x]-x==0.

Andrzej Kozlowski

Tokyo, Japan

On 28 Nov 2006, at 20:03, bobbaillie at frii.com wrote:

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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