* Let $a\_{n}$ be the sequence satisfying $a\_{1}=a\_{2}=1$ and $ a\_{n}=\tfrac{1}{2} (a\_{n-1}+\tfrac{2}{a\_{n-2}}) $ for $n\geq 3$. Then for all $n\in \mathbb{N}$, $1\leq a\_{n} \leq 2$

For $n=3$, then we have $1\leq a\_n\leq 2.$ 

Now assume for $n$ holds. Show for $n+1$ holds.

So

$$ a\_{n+1}=\tfrac{1}{2} (a\_{n}+\tfrac{2}{a\_{n-1}}) $$

**Then, what should I do now?**