Given that $\frac{1}{1-x}={\displaystyle \underset{n=0}{\overset{}{}}}{x}^n$ with convergence in $(-1,1),$ find the power series for $\frac{x}{1-8x^7}$ 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$)$:

Given that $\frac{1}{1-x}={\displaystyle \underset{n=0}{\overset{}{}}}{x}^n$ with convergence in $(-1,1),$ find the power series for $\frac{x}{1-8x^7}$ 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$)$: $$ to $x=,$ right end included $($enter Y or N $)$: $$