The sequence ${a_n}$ is defined by $a_1=2$, and
$a_{n+1}= {1\over2}(a_n+{2\over{a_n}})$ for $n≥1$. Assuming $a_n$ converges, find its limit.
I've found that the limit is $\sqrt2$ just by plugging a couple points, but not sure how to figure this out without plotting points (ie. by taking $\lim_{n\to\infty}S_n$) but I can't seem to figure out a formula for $a_n$ either.