1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

7. 1 • UNIFORM CONVERCENCE 253

An immediate consequence of Theorem 7.2 is Corollary 7.1.

t Corollary 7 .1 For each r, 0 < r < 1, the geometric series converges uniformly
on the closed disk Dr (O). •

Theorem 7.3 gives important properties of uniformly convergent sequences.