Chapter B.1, Problem 67E

If A is a positive real number, the terms of the sequence defined by

     $a_1=\frac{A}{2}and{a}_n=\frac{1}{2}\left(a_{n-1}+\frac{A}{a_{n-1}}\right)forn\ge 2$

can be used to approximate $\sqrt{A}$ to any decimal place accuracy desired. In Problems 67 and 68, compute the first four terms of this sequence for the indicated value of A, and compare the fourth term with the value of $\sqrt{A}$ obtained from a calculator.

67.    A = 2