$a_1=1$, $a_{n+1}=\frac{1}{2}\left(a_n+\frac{2}{a_n}\right)$. Show that the sequence is decreasing
$a_1=3$ and $a_{n+1}=\frac{a_n}{2} + \frac{1}{a_n}$. Show that it monotonically decreases and find the limit.