q$7$ Given that $\frac{1}{1-x}={\displaystyle \underset{n=0}{\overset{}{}}}{x}^n$ with convergence in $(-1,1),$ find the power series for $\frac{1}{1-7x^6}$ with center

$0.$

${\displaystyle \underset{n=0}{\overset{}{}}}$

Identify its interval of convergence. The series is convergent from

$x=,$ left end included $($enter Y or N $)$: $$

to $x=,$ right end included $($enter Y or N $)$: $$