下列结论正确的是( ).
$\text{A.}$ 若$\left\{a_n\right\}$有界, $\lim _ {n \rightarrow \infty }b_{n} $存在，则$ \lim _ {n \rightarrow \infty }a_nb_n $存在.
$\text{B.}$ 若$\left\{a_n\right\}$有界. ,$\lim _ {n \rightarrow \infty }b_{n} =0$, 则 $ \lim _ {n \rightarrow \infty }a_nb_n =0 $.
$\text{C.}$ 若$\left\{a_n\right\}$ 无界,$\left\{b_n\right\}$无界,则$\left\{a_nb_n\right\}$无界
$\text{D.}$ 若$\left\{a_n\right\}$为无穷小数列,$\left\{b_n\right\}$无界,则$\lim _ {n \rightarrow \infty }b_{n} =0$, 则 $ \lim _ {n \rightarrow \infty }a_nb_n =0$