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

• To: mathgroup at smc.vnet.net
• Subject: [mg31926] Re: Very simple limit, why doesn't it evaluate?
• From: "Mirek Gruszkiewicz" <gruszkiewicz at ornl.gov>
• Date: Wed, 12 Dec 2001 04:14:10 -0500 (EST)
• Organization: Oak Ridge National Lab, Oak Ridge, TN
• References: <9v49pp$n1v$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Jacek Dziedzic" <dust-NOSPAM- at tenbit.pl> wrote in message
news:9v49pp$n1v$1 at smc.vnet.net...
> 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
>
>
>

If your example stunned you, be careful with these:

Limit[2^n, n -> \[Infinity]]
is left unevaluated by Mathematica 4.
NLimit returns 2.

Limit[2^(n+1), n -> \[Infinity]]
returns Infinity

Limit[(2^(n+1))/2, n -> \[Infinity]]
returns Limit[2^n, n -> \[Infinity]]

Limit[(2^(n+1))/4, n -> \[Infinity]]
returns Infinity

and so on.


MG