Given that $\frac{1}{1-x}={\displaystyle \underset{n=0}{\overset{}{}}}{x}^n,$ which converges for $x$ in $(-1,1),$ find the power series representation for the function $f(x)=\frac{1}{1-7x}$ centered at $a=0$ and find its interval of convergence.

The power series for the function is $f(x)=\frac{1}{1-7x}={\displaystyle \underset{n=c}{\overset{}{}}}$ help $($formulas$)$

Interval of convergence is help $($intervals$)$