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MathGroup Archive 2001

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Re: Very simple limit, why doesn't it evaluate?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31917] Re: [mg31909] Very simple limit, why doesn't it evaluate?
  • From: Otto Linsuain <linsuain at andrew.cmu.edu>
  • Date: Wed, 12 Dec 2001 04:13:57 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I could reproduce the error, and fix it. For some reason one has to make
the numbers real (i.e. machine precision, rather than infinite precision).
It is enough to write 4. instead of 4 or 3. instead of 3 or 5. instead of
5 and Mathematica is happy to print its little infinity symbol.

However, I tried Limit[4^n/3^n, n->Infinity]

Again, returns it unevaluated. After changing the 4 to 4. and so on, the
best answer I got was

Limit[1.33333^n, n -> Infinity]

I know the story about the precision and such, but the limit of this
things does not depend significantly on the precision of the calculation.
I cannot see how the errors could pile up to prevent this thing from
diverging!

Otto Linsuain.

On Tue, 11 Dec 2001, Jacek Dziedzic wrote:

> It stunned me that the Mathematica 3.0 returns this very simple limit
> unevaluated:
> 4^(n+3)/(3^(n+4)-5), with n -> infinity.
>
> Moreover, the NLimit function returns 1.0756... which is a rather poor
> approximation of infinity (the expected result)... Well I can understand
> that NLimit is numerical and can't be relied on, but why does the original
> Limit[] die on that? Or am I doing anything wrong?
>
> - Jacek Dziedzic
>
>
>
>



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