Show that this converges and where it converges too.

$\displaystyle a(n+1) = 1/2(an +3/an)$. given that (a1=2)

Well I found out where it converges too by starting with a1=2 that gave me a2 = 7/4, a3 = 97/56 and that is very close too sqrt:3 so that is where it goes. (Thinking).

I am however not sure how to "show" that it converges...?

A general hint on how to show anything here is fine I really wan´t too solve these by myself...