Answer
See below.
Work Step by Step
A sequence $\{a_{n}\}$ with the property that $a_{n}\leq a_{n+1}$ for all $n$ is called a nondecreasing sequence.
If $a_{n}\geq a_{n+1}$ for all $n$, then it is called nonincreasing.
A sequence is monotonic if it is either nondecreasing or nonincreasing.
By Theorem 6, The Monotonic Sequence Theorem,
if a sequence $\{a_{n}\}$ is both bounded and monotonic, then the sequence converges.
$a_{n}=\displaystyle \frac{1}{n}\qquad \left\{1,1/2,1/3,...\right\}$
is nonincreasing and bounded (no term is less than 0), so it converges (to 0).
$a_{n}=2-\displaystyle \frac{1}{n} \qquad \left\{1,3/2,5/3,7/4,...\right\}$
is nondecreasing and bounded (no term is greater than 2), so it converges (to 2).
