3. (a) Show that the power series * does not converge uniformly for |2| < 1. k=1 (b) Show that the power series kz* does not converge at any point on the unit circle |z| = 1. |3D k=1 (c) Show that the power series converges uniformly for |z| = 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
icon
Related questions
Question

Please please answer all subparts.

I will really upvote

3. (a) Show that the power series >* does not converge uniformly for |2| < 1.
(b) Show that the power series 2 kz*does not converge at any point on the unit circle |z| = 1.
%3D
k=1
(c) Show that the power series
converges uniformly for |2| = 1.
Transcribed Image Text:3. (a) Show that the power series >* does not converge uniformly for |2| < 1. (b) Show that the power series 2 kz*does not converge at any point on the unit circle |z| = 1. %3D k=1 (c) Show that the power series converges uniformly for |2| = 1.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer