# Algebra: Convergence of Series

Not what you're looking for?

Please help with the following problem. This problem is from Advanced Calculus II class. It is also an introduction to real analysis.

Consider the series n = 1 to infinity 1/( 1 + n^2 x)

(a) For what values of x in R does the series converge absolutely?

(b) On what intervals of R does it converge uniformly?

(c) On what intervals of R does it fail to converge uniformly?

(d) Is the series bounded on R?

Please I want detailed answers with full explanation..after all I want to learn not just have the right answer. I appreciate your help. Thanks.

##### Purchase this Solution

##### Solution Summary

This posting helps with basic algebra problems. The calculations include values, intervals, uniform convergence. Step by step calculations are given for each problem.

##### Solution Preview

a) For what values of x in R does the series converge absolutely?

Case 1. Let x= 0.

Then the series equals n so it is not convergent, abs converges or uniformly convergent.

Case 2.

Let an = 1/( 1 + n^2 x).

Now Σ|an| converges.

Now Σ|an| < Σ 1/|n²x| = 1/|x| Σ 1/n² which is ...

###### Education

- BSc, University of Bucharest
- MSc, Ovidius
- MSc, Stony Brook
- PhD (IP), Stony Brook

###### Recent Feedback

- "Thank you "
- "Thank You Chris this draft really helped me understand correlation."
- "Thanks for the prompt return. Going into the last meeting tonight before submission. "
- "Thank you for your promptness and great work. This will serve as a great guideline to assist with the completion of our project."
- "Thanks for the product. It is an excellent guideline for the group. "

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Probability Quiz

Some questions on probability

##### 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.

##### 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.