Sequences — limit superior of a recursively defined sequence

For a non-negative real number $a$, let $\sqrt{a}$ denote its non-negative square-root. Consider the sequence $\{x_n\}_{n\ge1}$ defined by

$$x_1=1\quad\text{and}\quad x_{n+1}=\sqrt{1+\frac{x_n^2}{n}}\quad\text{for }n\ge1 .$$

Which of the following statements is true?