Differences between recursions and limit

*To*: mathgroup at smc.vnet.net*Subject*: [mg60509] Differences between recursions and limit*From*: "anbra1" <xyxanbra1 at tiscalixxxyxxx.it>*Date*: Mon, 19 Sep 2005 04:45:30 -0400 (EDT)*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

**Follow-Ups**:**Re: Differences between recursions and limit***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Differences between recursions and limit***From:*<bsyehuda@gmail.com>