Purchase Solution

Show that multiplication of an absolutely convergent series and bounded series is convergent.

Not what you're looking for?

Ask Custom Question

Suppose the series ak (the k is subscript) converges absolutely and that the series bk is bounded.

Show that the series ak*bk converges absolutely.

Purchase this Solution

Solution Summary

Multiplication of an absolutely convergent series and bounded series is shown to be convergent.

Solution Preview

Since bk is bounded, we know that there exists some bound M such that

|bk| < M for all k
( |bk| is "modulus of bk")

We also know that sum(|ak|)=N, (where N, of course, is ...

Purchase this Solution


Free BrainMass Quizzes
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.

Exponential Expressions

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

Graphs and Functions

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

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.