$2\mathrm{.}5$ Homework

A sequence is an infinite, ordered list of numbers that is often defined by a function. For example, the sequence $\{2,4,6,8,$dots$\}$ is specified by the function $f(n)=2n,$ where $n=1,2,3,$dots. The limit of such a sequence is lim $f(n),$ provided the limit exists. All the limit laws for limits at infinity may be applied to limits of sequences. Find the limit of the following sequence, or state that the limit does not exist.

$\{5,\frac{5}{2},\frac{5}{3},\frac{5}{4},1,\frac{5}{6},$dots$\},$ which $is$ defined $byf(n)=\frac{5}{n}$ for $n=1,2,3,$dots

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.$ The limit of the sequence is $.$

B$.$ The limit does not exist and is neither $$ nor $-.$