Solution
= Solution
{c}
\b[False.] Choose the positive <sequence>
$$
\boxed{a_n=1+\frac1{\sqrt n}.}
$$
It has <limit of a sequence> one, but <Bernoulli's inequality> gives
$$
a_n^n=\left(1+\frac1{\sqrt n}\right)^n\geq1+\sqrt n\longrightarrow+\infty.
$$
Thus $(a_n^n)$ is not a <bounded sequence>.