######################## PROBLÈME 1: #########################

#@# solution récursive
u := proc(n)
  options remember;  #@# nécessaire !
  111 - 1130/u(n-1) + 3000/(u(n-2)*u(n-1));
end:
u(0) := 11/2:
u(1) := 61/11:

#@# solution itérative
u2 := proc(n)
  local t, i, n_1, n_2;
  n_2 := u2(0);
  n_1 := u2(1);
  for i from 2 to n do
    t := 111 - 1130/n_1 + 3000/(n_2*n_1);
    n_2 := n_1;
    n_1 := t;
  od;
  t;
end:
u2(0) := 11/2:
u2(1) := 61/11:

#@# solution approchée (utilise la variable globale d, supposée entière)
d := 20:
u3 := proc(n)
  global d;
  options remember;
  evalf(111 - 1130/u3(n-1) + 3000/(u3(n-2)*u3(n-1)), d);
end:
u3(0) := evalf(11/2, d):
u3(1) := evalf(61/11, d):

#@# solution approchée (propre, évite de modifier/restaurer Digits)
ua := proc(n, d)
  local u;
  u := proc(n)
    options remember;
    evalf(111 - 1130/u(n-2) + 3000/(u(n-2)*u(n-1)), d);
  end;
  u(0) := evalf(11/2, d);
  u(1) := evalf(61/11, d);
  u(n);
end:

eq := (111 - 1130/x + 3000/(x*x) = x):
solve (eq, x);