Let $g(x)=1+4x+x^2+4x^3+x^4+$cdots, where the coefficients are $c_{2n}=1$ and $c_{2n+1}=4$ for $n0.$

$($a$)$ Find the interval of convergence of the series. $($Enter your answer using interval notation.$)$

$($b$)$ Find an explicit formula for $g(x).$

$g(x)9\mathrm{.}8$ wuestion $20$