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


"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





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