Use the Ratio Test to determine the convergence or divergence of the infinite series.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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Use the Ratio Test to determine the convergence or divergence of the infinite series.
Transcribed Image Text:Use the Ratio Test to determine the convergence or divergence of the infinite series.
Expert Solution
Step 1

Given:

Calculus homework question answer, step 1, image 1

Step 2

Ration Test:

The usual form of the test makes use of the limit 

Calculus homework question answer, step 2, image 1

 

  • if L < 1 then the series converges absolutely (and therefore the series is convergent);
  • if L > 1 then the series is divergent;
  • if L = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case.

 

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