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?.