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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>