Show by induction:

$\displaystyle x_{n+2}=\frac{x_{n}+x_{n+1}}{2}$

$\displaystyle x_{1}=0, x_{2}=1,$

that $\displaystyle 0\leq x_{n}\leq 1$$\displaystyle , n= 1,2,3,...$

If i suppose that $\displaystyle 0\leq x_{k+2}=\frac{x_{k}+x_{k+1}}{2}\leq 1$ is valid,

then i want to show that $\displaystyle 0\leq x_{k+3}=\frac{x_{k+1}+x_{k+2}}{2}\leq1$ is valid by using my assumption. But i can't find a way to do this.

Maybe this is totally wrong way to do it.

/regards