![[Graphics:Images/UniformConvergenceMod_gr_122.gif]](../Images/UniformConvergenceMod_gr_122.gif){kind=small}
), the
geometric series ![[Graphics:Images/UniformConvergenceMod_gr_123.gif]](../Images/UniformConvergenceMod_gr_123.gif){kind=small}
converges
uniformly on the closed disk ![[Graphics:Images/UniformConvergenceMod_gr_124.gif]](../Images/UniformConvergenceMod_gr_124.gif){kind=small}
. Corollary 7.1. For
each r, (where ), the
geometric series converges
uniformly on the closed disk .
Proof.
Corollary 7.1 is mentioned in the book.
Complex Analysis for Mathematics and Engineering