Hi everybody

$\displaystyle f(x)=Arctan\frac{1}{x}; x \in [ \frac{\sqrt{3}}{3};1] $

$\displaystyle \{{ U_0=\frac{\sqrt{3}}{3} \atop U_{n+1}=f(U_n)}, \forall n \in \mathbb {N}$

I must show that $\displaystyle (\forall n \in \mathbb{N}): \frac{\sqrt{3}}{3} \le U_n \le 1$ (i used induction but i don't know how to show that: $\displaystyle \frac{\sqrt{3}}{3} \le U_{n+1} \le 1)$

Can you help me please?