Purchase Solution

Infinite series

Not what you're looking for?

Ask Custom Question

If series Sum(an) and Sum(bn) with positive terms are convergent, is the series Sum(an*bn) converegent?

Note:
1. Sum replaces the symbol for summation
2. an and bn are nth elements of the two series

Purchase this Solution
Solution Summary

This shows how to determine if a series based on thes um of two other series is convergent.

Solution Preview

Consider the series Sum(an).
1.We are given that Sum(an) is convergent
2.Claim {an} is a bounded sequence,
i.e. there exists M such that for
all n |an|<=M. (Since all ...

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.

Exponential Expressions

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

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.

View More Free Quizzes
Related BrainMass Solutions

  • Infinite Taylor Series

    142384 Infinite Taylor Series (b) Find an infinite series for ln 2 by setting x = 1/2. Now, find another infinite series for ln 2 by setting x = 2. (c) Find an infinite series for pi by setting x = 1 + i. Infinite Taylor Series.

  • Infinite series sum

    99150 Proof of sum of a given infinite series of constants (closed form). The sum of the infinite series, 1/2^2 - 2/3^2 + 3/4^2 - 4/5^2 + ... is given as pi^2/12 - log 2 on pages 64-65 in the book "Summation of Series" by L. B. W.

  • Convergence Tests for Series : Comparison test, limit comparison test, integral test, and nth term test

    72218 Convergence Tests for Series : Comparison test Use only the comparison test, limit comparison test, integral test, and nth term test to test for convergence or divergence infinite series(n=2 to infinity) sqrt(25n+4/n^3-n) infinite series

  • Closed Form for an Infinite Series

    Does the series converge for x=i? This series is a geometric series and so its infinite sum is 1/(1-x) and this is its closed form.

  • Infinite Series : Convergence and Divergence (8 Problems)

    series is convergent or divergent: b) Determine whether each of these infinite series are convergent or divergent.

  • Matrices and Infinite Series Method

    This solution has step-by-step calculations in applying the infinite series methods on the matrices aforementioned to finally determining e^AT.

  • infinite series

    29316 Real Analysis - Infinite Series; Convergent Decide whether or not the following infinite series converge, in each case prove your result (by using theorems) *(Please see attachment for series).

  • Geometric Series and Sums

    Suppose, if we take first term a=2, number of terms 4 and r = 2 then sum In case of infinite series then If we take a =15 and r = ½ Then series become Part B Can you find a specific geometric series that sums to -30 ?

  • Infinite series method

    91630 Infinite Series Method 2nd order DE The following second order Differential Equations must be solved with the appropriate Infinite Series Method.

  • Infinite Series : Geometric Progression

    Infinite series and geometric progressions are investigated and discussed.

View More Related Solutions