Suppose that A > 0 is a given real number. Define the sequence {$\displaystyle a_n$}$\displaystyle n \in N$ recursively by:

$\displaystyle a_1$ is a positive real number; $\displaystyle a_{n+1} = \frac{1}{2} (a_n + \frac{A}{a_n})$.

Prove that {$\displaystyle a_n$}$\displaystyle n \in N$ converges to $\displaystyle \sqrt{A}$

No clue where to start...