Answered: 1)"n п — 3 n n=4

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 52E

See similar textbooks

Related questions

Question

Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series.

Expert Solution

Step 1

Given:

$\sum_{n = 0}^{\infty} \frac{{(- 1)}^{n} n}{(n - 3)}$

Step 2

Alternating Series Test:

Suppose that we have a series $\underset{n}{\sum a_{n}}$ and either $a_{n} = {(- 1)}^{n} b_{n}$ or $a_{n} = {(- 1)}^{n + 1} b_{n}$ where $b_{n} \geq 0$ for all n. Then if,

$1 . \lim_{n \to \infty} b_{n} = 0$ and,

$2 . \{b_{n}\}$ is a decreasing sequence

the series $\sum_{n} a_{n}$ is convergent

This test does not say about divergence.

Step by step

Solved in 4 steps

Knowledge Booster

$Series$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage