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MathGroup Archive 2005

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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



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