Re: Differences between recursions and limit

*To*: mathgroup at smc.vnet.net*Subject*: [mg60728] Re: Differences between recursions and limit*From*: "anbra1" <xyxanbra1 at tiscalixxxyxxx.it>*Date*: Mon, 26 Sep 2005 01:36:06 -0400 (EDT)*References*: <dgm01k$njm$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

> Please, > I want to know > why these two recursions,doing the same thing, > are the first one much more slow than the second > ------------------------- > x[0]=0; > x[k_] := .25 *(1 + x[k-1] + (x[k-1])^2 + (x[k-1])^3); > For[k=1,k<12,Print[k," ",SetPrecision[x[k],30]];k++] > ------------------------- > a=0; > For[k=1,k<12,k++, > b= .25 (1 + a + a^2 + a^3);a:=b;Print[k," ",SetPrecision[b,30]]] > ------------------------- > Another question > How can I calculate > the limit of this recursion for k->Infinite ? > Thank you all Many thanks to Andrzej Kozlowski,Bob Hanlon,Peter Pein and to bsyehuda,Jens-Peer Kuska,albert and shizp for your precious answers