Can the LCT be Used Without Showing the Comparison Test Will Not Work?

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SUMMARY

The Limit Comparison Test (LCT) can be applied without demonstrating that a traditional Comparison Test fails. If both tests are applicable, they yield the same convergence results. This confirms that the choice of test does not affect the outcome regarding series convergence.

PREREQUISITES
  • Understanding of series convergence concepts
  • Familiarity with the Comparison Test and Limit Comparison Test
  • Basic knowledge of mathematical limits
  • Ability to analyze series using convergence tests
NEXT STEPS
  • Study the formal definitions and conditions of the Comparison Test
  • Explore the Limit Comparison Test in detail with examples
  • Review convergence criteria for series in calculus
  • Practice applying both tests on various series to reinforce understanding
USEFUL FOR

Students studying calculus, particularly those focusing on series convergence, as well as educators teaching convergence tests in mathematics.

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Homework Statement


I was just wondering that when applying a comparison test or a limit comparison test, do i have to show that a comparison test does not work in order to use a LCT? Also, if i directly use LCT, will i get the same answer as in the regular comparison test?
Thanks.

Homework Equations





The Attempt at a Solution

 
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You do not have to first show that a comparison test will not work. If both tests are applicable then your result should be the same.

Convergence is independent of the test you use.
 

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