2. Let the sequence $\left\{a_{n}\right\}$ satisfy
$$
a_{1}>1, a_{n+1}=a_{n}+\frac{1}{a_{n}^{2}} \text {. }
$$

Then the sequence $\left\{a_{n}\right\}()$.
(A) is bounded and decreasing
(B) is bounded and increasing
(C) is unbounded and increasing
(D) is unbounded and decreasing