O15-C902
> restart:
> f:=(t,u)->111-1130/u+3000/t/u;

> u:=array(0..20);u[0]:=2;u[1]:=-4;

                       u := array(0 .. 20, [])


                              u[0] := 2


                              u[1] := -4

> for k from 2 to 20 do u[k]:=f(u[k-2],u[k-1]) od:map(evalf,u);

  array(0 .. 20, [

        (0) = 2.

        (1) = -4.

        (2) = 18.50000000

        (3) = 9.378378378

        (4) = 7.801152738

        (5) = 7.154414481

        (6) = 6.806784737

        (7) = 6.592632769

        (8) = 6.449465934

        (9) = 6.348452057

        (10) = 6.274438598

        (11) = 6.218695740

        (12) = 6.175837305

        (13) = 6.142359081

        (14) = 6.115883067

        (15) = 6.094739439

        (16) = 6.077722305

        (17) = 6.063940322

        (18) = 6.052721761

        (19) = 6.043552110

        (20) = 6.036031881

        ])

> solve(r^3-111*r^2+1130*r-3000);

                              5, 6, 100

> p:=n->a*5^n+b*6^n+c*100^n;

> s:=solve({p(0)=2,p(1)=u[2]*p(0),p(2)=u[3]*p(1)},{a,b,c});

                    s := {c = 0, a = -25, b = 27}

> subs(s,p(n));

                                 n       n
                            -25 5  + 27 6

> uu:=subs(s,p(n-1)/p(n-2));limit(uu,n=infinity);

                              (n - 1)       (n - 1)
                         -25 5        + 27 6
                   uu := --------------------------
                              (n - 2)       (n - 2)
                         -25 5        + 27 6


                                  6

>