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Re: Differences between recursions and limit


> 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



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