1. The general formula of recursive formula iteration method can be expressed as continued fraction.

A = Li Man = a+1/an =1+1/a.

A=(a+√(a*a+4))/2

2.bn=an-A

To prove the original proposition, just prove (an+ 1)-A =(A-an)/A*an.

Just prove (an+1)-a =1/an-1/a.

Just prove an+1= a-1/a+1/an.

Because A= 1+ 1/A, A- 1/A= 1.

Substituting the above formula is the original condition.

Certificate of completion