Find analytically the sequence of iterations $x_n$ for Newton's method applied to the function $f(x) = x^2$ with the starting point $x_0 = 1$.

Question

Find analytically the sequence of iterations $x_n$ for Newton's method applied to the function $f(x) = x^2$ with the starting point $x_0 = 1$?

How would you do this, we can't use the recursive formula for Newton's method right? Thanks.