Consider the Newton-Raphson method applied to approximate the square root of a positive number α. A recursion relation for the error en = xn -√α is given by
1
\(e_{n+1}=\frac{1}{2}\left(e_n+\frac{α}{e_n}\right)\)
2
\(e_{n+1}=\frac{1}{2}\left(e_n-\frac{α}{e_n}\right)\)
3
\(e_{n+1}=\frac{1}{2} \frac{e_n^2}{e_n+√{α}}\)
4
\(e_{n+1}=\frac{e_n^2}{e_n+2 √{α}}\)