Question

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

Answer 1

`\frac4{x+2}=\frac2{1-\left(-\frac x2\right)}=2\displaystyle\sum_(n\ge0)\left(-\frac x2\right)^n`

which is valid for
`\left|-\frac x2\right|<1`, or
`|x|<2`.