Answer
1-3$\Sigma\frac{(-1)^nx^n}{2^{n+1}}$
Work Step by Step
$\frac{x-1}{x+2}$ can be rewritten as = $\frac{x+2-3}{x+2}$
1 - $\frac{3}{x+2}$ = 1 - $\frac{3}{2+x}$
1 - $\frac{3}{2}$($\frac{1}{1+\frac{x}{2}}$)
Geometric series with r=$\frac{-x}{2}$
Radius of Convergence = -2, Interval of Convergence (-2,2)
