Question 1
Define the sequence $\{x_n\}$ by $x_1=a\ge1$ and
$$x_{n+1}=1+\ln\frac{x_n(x_n^2+3)}{1+3x_n^2}.$$
Prove that the sequence converges and determine its limit.
$$x_{n+1}=1+\ln\frac{x_n(x_n^2+3)}{1+3x_n^2}.$$
Prove that the sequence converges and determine its limit.