Did you try the ratio test. When you do and take the limit,
I may as well finish.
Diverges if x<-2 or of x>0
Check the endpoints:
If we enter in x=-2 into our series we get , converges. (converges to )
If we enter in x=0, we get , diverges.
So, the interval of convergence is [-2,0) with radius of 1
My assessment agrees with MS except are you sure when x=0 it converges?.