Question 3
Define $x_0,x_1,x_2,\ldots$ by $x_0=a$, where $0\lt a\lt 1$, and
$$x_{n+1}=\frac4{\pi^2}\left(\arccos x_n+\frac\pi2\right)\arcsin x_n.$$
Prove that the sequence converges and determine its limit.
$$x_{n+1}=\frac4{\pi^2}\left(\arccos x_n+\frac\pi2\right)\arcsin x_n.$$
Prove that the sequence converges and determine its limit.