2. Given the positive sequence $\left\{a_{n}\right\}$ :
$$
a_{1}=\alpha<\frac{\sqrt{2}}{2}, a_{n+1}^{2}=\frac{2 a_{n}^{2}}{1+2 a_{n}^{2}} \text {. }
$$

Then $\left\{a_{n}\right\}$ ).
(A) increasing and bounded above
(B) increasing and unbounded above
(C) decreasing and bounded below
(D) decreasing and unbounded below
2. A.
$$
a_{1}0,
$$
so, $a_{n+1}>a_{n}$, the sequence $\left\{a_{n}\right\}$ is increasing.