Find the interval of convergence of the power series. $($Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.$)$

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{(-1{)}^{n+1}(x-3{)}^n}{n{8}^n}$