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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



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