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

• To: mathgroup at smc.vnet.net
• Subject: [mg31920] Re: [mg31909] Very simple limit, why doesn't it evaluate?
• From: BobHanlon at aol.com
• Date: Wed, 12 Dec 2001 04:14:00 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

In a message dated 12/11/01 2:22:26 AM, dust-NOSPAM- at tenbit.pl writes:

>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?
>

I have version 4.1; however, this will probably work in version 3.

Needs["Calculus`Limit`"];

Limit[4^(n+3)/(3^(n+4)-5), n->Infinity]

Infinity

Oddly, version 4.1 does not show the add-on Calculus`Limit in the Help 
Browser.


Bob Hanlon
Chantilly, VA  USA