//     Suites u_n=f(n)

f:= x -> sin(x)/(x^2+1)
for j from 1 to 10 do
      u0:=f(j)
      print(j, u0, evalf(u0))
end_for

f:= sin(x)/(x^2+1)
for j from 1 to 10 do
      u0:=subst(f,x=j)
      print(j, u0, evalf(u0))
end_for

plotfunc(f(x), x = -10..10)
plotfunc(f(x), x = 0..40)

f:= x -> sin(x)/(x^2+1);
plotseq(f(x),1,20)


// Suites recurrentes - 1 : u_(n+1)=f(u_n)

f:= x -> sqrt(x+1)

u0:=0.5;
j:=0;
N:=20;

print(evalf(u0));
t:=u0;
for j from 1 to N do
      u0:=evalf(f(u0))
      t:=t,u0:
      print(j,u0)
end_for

plotseq(f(x),0.5,20)