Question 1
Let the sequence $\{x_n\}_{n=1}^{+\infty}$, with $|x_1|\lt 1$, be defined by
$$x_{n+1}=\frac{-x_n+\sqrt{3-3x_n^2}}2.$$
(a) What condition on $x_1$ is necessary for every term of this sequence to be positive?
(b) Is this sequence periodic? Explain your answer.
$$x_{n+1}=\frac{-x_n+\sqrt{3-3x_n^2}}2.$$
(a) What condition on $x_1$ is necessary for every term of this sequence to be positive?
(b) Is this sequence periodic? Explain your answer.