       Re: Bug in Limit ?

• To: mathgroup at smc.vnet.net
• Subject: [mg25991] Re: [mg25951] Bug in Limit ?
• From: BobHanlon at aol.com
• Date: Wed, 15 Nov 2000 02:09:42 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 11/14/00 4:27:00 AM, mtpagesj at lg.ehu.es writes:

>This looks like a bug in the package Calculus`Limit`
>
>In:= \$Version
>Out= "4.0 for Power Macintosh (July 20, 1999)"
>
>In:= << Calculus`Limit`
>
>In:= Limit[(2^(n + 1) + 3^(n + 1))/(2^n + 3^n), n -> Infinity]
>Out= 9
>
>The calcultion was done in a G4. The same result was obtained in version
>3
>under windows.
>

It is definitely wrong.  It does much better if you simplify the expression
before taking the limit.

Needs["Calculus`Limit`"];

Limit[(2^(n + 1) + 3^(n + 1))/(2^n + 3^n), n -> Infinity]

9

(2^(n + 1) + 3^(n + 1))/(2^n + 3^n) // FullSimplify

3 - 1/(1 + (3/2)^n)

Limit[%, n -> Infinity]

3

Plot[(2^(n + 1) + 3^(n + 1))/(2^n + 3^n), {n, 0, 20}];

Bob Hanlon

```

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