Infinite geometric series and convergence I have been given the infinite geometric series-:
$$
2-\frac 4x + \frac8{x^2}
-\frac{16}{x^3}+\dots
(x\neq 0)$$
I am asked to


Find the convergence area to the sequence
Find the sum $S(x)$ and the domain


I'm completely stuck as to how I should proceed! 

When I use $X$ values greater than $0$ and less than $1$ it seems as though the series alternates between $-\infty$ and $+\infty$  as I approach infinity...

With $X$ values less than $0$ it seems to approach $+ \infty$?

I have no idea, could some kind soul shine a light?
The series is $\sum_{n=0}^\infty a_n$, for  $a_n=2(\frac{-2}{x})^n$.

A good first step is to compute $\frac{a_{n+1}}{a_n}$ and simplify.  If this is constant, you have a geometric series you can sum with the formula.  If not, you can apply the ratio test.
The sum 
$S(x) = 2(1+2/x)^{-1}$