Given a_1\, = \, \dfrac{1}{2}\left ( a_0 \, + \, \dfrac{A}{a_0} \right ) \, , \,a_2\, = \, \dfrac{1}{2}\left ( a_1 \, + \, \dfrac{A}{a_1} \right )
and a_{n \, + \, 1}\, = \, \dfrac{1}{2}\left ( a_n \, + \, \dfrac{A}{a_n} \right )
Find n\geq \, 2 where a > 0, A > 0, prove that
\dfrac{a_n \, - \, \sqrt{A}}{a_n \, + \, \sqrt{(A)}}\, = \, \left (\dfrac{a_1 \, - \, \sqrt{A}}{a_1 \, + \, \sqrt{(A)}} \right )^{2^{n \, - \, 1}}
using mathematical induction.