Question

Find the power series expansion for f(x)= 4/(x+2); x doesn't equal 2, centered at 0

Answer 1

$\dfrac4{x+2}=\dfrac2{1-\left(-\frac x2\right)}=2\displaystyle\sum_{n\ge0}\left(-\frac x2\right)^n$

which is valid for $\left|-\dfrac x2\right|$, or $|x|$.