Is a Power Series More Likely to Diverge Further from Its Radius of Convergence?

[fiziksfun]

If a power series, $$\sum$$c(subk)*x$$^{k}$$ diverges at x=-2, then it diverges at x=-3. True or False?

I said true, but was confused by my reasoning. Does anyone have any suggestions?

 

[Dick]

Think about 'radius of convergence'.