Answer
$\left\{ {\frac{1}{{2n + 1}}} \right\}$ is decreasing for all $n \ge 0$
Work Step by Step
By definition on page 535:
$\left\{ {{a_n}} \right\}$ is increasing if ${a_n} < {a_{n + 1}}$ for all $n$.
$\left\{ {{a_n}} \right\}$ is decreasing if ${a_n} > {a_{n + 1}}$ for all $n$.
Since ${a_n} = \frac{1}{{2n + 1}}$ satisfies ${a_n} > {a_{n + 1}}$ for all $n \ge 0$, by definition, $\left\{ {{a_n}} \right\}$ is decreasing in this interval.
