The infinite sum $S$ is defined as

1. Find the range of $x$ for which $S$ converges.

2. Show that $S$ be expressed in the form

   $$\frac{1}{q(x)}$$

   where $q(x)$ is a quadratic to be found.

For (a), note that the common ratio is $r=(1-x{)}^2$ and we must have $|r|<1$ for convergence to take place.

Again for (a), $|(1-x{)}^2|$ is simply equal to $(1-x{)}^2$, so we need to solve the inequality

This is a quadratic inequality

For (b), use the formula for $S_{\mathrm{\infty }}$.