HI everybody,

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

I showed that $\displaystyle 1\le U_n\le \frac{3}{2}$, but i don't know how to show that

$\displaystyle |U_{n+1}-U_n|\le \frac{1}{4}|U_n - U_{n-1}|$

Can you help me please???

Thanks.