# Proving the Root Test

Not what you're looking for?

A) Prove root test " lim(sqrt|An)|)=L as n goes to infinity" assuming ratio test "lim(|An+1)|/|A n|)=L as n goes to infinity"

ps. {An} is a sequence of non-zero complex numbers

b) Prove that although the following power series have R=1 sum(nz^n) does not converge on any point of the unit circle.

##### Purchase this Solution

##### Solution Summary

The root test is proven assuming ratio test.

##### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Problem:

a) Prove root test " lim(sqrt|An)|)=L as n goes to infinity" assuming ratio test "lim(|An+1)|/|A n|)=L as n goes to infinity"

ps. {An} is a sequence of non-zero complex numbers

b) Prove that although the following power series have R=1

sum(nz^n) does not converge on any point of the unit circle

Solution:

a) First off all, I have to make a correction to the above statement:

it is not sqrt|An| under the limit, but |An|^(1/n) or in other words, it is not "square" root, but root of order "n" (or fractional power).

Now, we can rephrase the theorem which we ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Solving quadratic inequalities

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

##### Exponential Expressions

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

##### 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.

##### Probability Quiz

Some questions on probability

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts