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Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.3: Rules For Addition

Problem 43WE

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Question

Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.

Expert Solution

Step 1: Given that:

We need to use the Ratio Test to determine the convergence or divergence of the series.

Step 2: Ratio Test.

According to the ratio test, if for any series $a_{n}$ there exist,

$L = \lim_{n \to \infty} |\frac{a_{n + 1}}{a_{n}}|$

Such that the

Series converges if L<1
Series diverges if L>1
Limit fails if L=1, then the test is Inconclusive.

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