Corollary 4.3. If , then for all n, .
Exploration.
We can explore the situation for .
In general we have.
(c) 2006 John H. Mathews, Russell W. Howell
![[Graphics:Images/ComplexGeometricSeriesMod_gr_128.gif]](../Images/ComplexGeometricSeriesMod_gr_128.gif){kind=small}
, then
for all n, ![[Graphics:Images/ComplexGeometricSeriesMod_gr_129.gif]](../Images/ComplexGeometricSeriesMod_gr_129.gif){kind=small}
. , then
for all n, . ![[Graphics:../Images/ComplexGeometricSeriesMod_gr_130.gif]](../Images/ComplexGeometricSeriesMod_gr_130.gif){kind=small}
.![[Graphics:../Images/ComplexGeometricSeriesMod_gr_131.gif]](../Images/ComplexGeometricSeriesMod_gr_131.gif)
![[Graphics:../Images/ComplexGeometricSeriesMod_gr_132.gif]](../Images/ComplexGeometricSeriesMod_gr_132.gif)
![[Graphics:../Images/ComplexGeometricSeriesMod_gr_133.gif]](../Images/ComplexGeometricSeriesMod_gr_133.gif)
![[Graphics:../Images/ComplexGeometricSeriesMod_gr_135.gif]](../Images/ComplexGeometricSeriesMod_gr_135.gif)