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