Purchase Solution

Power series convergence

Not what you're looking for?

Ask Custom Question

Prove that a power series converges absolutely everywhere or nowhere on its circle of convergence.

Purchase this Solution

Solution Summary

Every complex power series has a certain radius of convergence, inside of which the series is guaranteed to converge. What happens on the very edge of this region, when the radius is equal to the radius of convergence? In general, we cannot say, but it is true that the series either converges absolutely everywhere or nowhere on the circle of convergence. The solution comprises a one page Word attachment, with equations written in Mathtype, proving this fact, and also giving an example of each case.

Purchase this Solution


Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.