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Given a1=1/2(a0+A/(a0)), a2=1/2(a1+A/(a1...

Given `a_1=1/2(a_0+A/(a_0)), a_2=1/2(a_1+A/(a_1))` and `a_(n+1)=1/2(a_n+A/(a_n))` for `n>=2`, where `a>0,A>0`. prove that `(a_n-sqrt(A))/(a_n+sqrt(A))=((a_1-sqrt(A))/(a_1+sqrt(A)))2^(n-1)`.

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