Convergence of a binomial expansion

Question

I have the binomial expansion $$1+(-1)(-2z)+\frac{(-1)(-2)(-2z)^2}{2!}+\frac{(-1)(-2)(-3)(-2z)^3}{3!}+...$$

Which simplifies down to $$1+2z+(-2z)^2+(-2z)^3$$

How do I find out if this binomial expansion converges for $|z|<1$?