Convergence at $\alpha$

Question

Let $$x_{n+1} = \frac{12}{1+x_n}$$ and let $\alpha = 3$. Does the iteration converge to $\alpha$ and if yes give the order of convergence?

So I check the derivative $|g'(\alpha)| = \left|\frac{-12}{(1+x_n)^2}\right|=\frac{3}{4} < 1$ so it converges to $\alpha$. The convergence is linear since $g' \neq 0$. Is this correct?

Answer 1

In fact this is correct, by the theorem of convergence.