Corollary 4.2. If  [Graphics:Images/ComplexGeometricSeriesMod_gr_92.gif],  the series  [Graphics:Images/ComplexGeometricSeriesMod_gr_93.gif] converges to [Graphics:Images/ComplexGeometricSeriesMod_gr_94.gif].  That is, if [Graphics:Images/ComplexGeometricSeriesMod_gr_95.gif] then  

            [Graphics:Images/ComplexGeometricSeriesMod_gr_96.gif],  
or equivalently,
            [Graphics:Images/ComplexGeometricSeriesMod_gr_97.gif].  

If  [Graphics:Images/ComplexGeometricSeriesMod_gr_98.gif],  the series diverges.

Proof.

Proof of Corollary 4.2 is in the book.

Complex Analysis for Mathematics and Engineering