Consider the power series in $x-4$ given by

$y={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^{n+1}}{(-4{)}^n}(x-4{)}^n$

a$)$ Calculate the limit $L=\underset{n}{lim}|\frac{a_{n+1}}{a_n}|$ to determine the radius of convergence $R$ of the power series.

$R=$

$$

b$)$ Determine the open interval of convergence in the form $(a,b).$ If it converges only for a single point, use the same value for both endpoints of the interval. If the radius is infinite, enter $-$oo and oo for the endpoints.

Open interval of convergence: $$