Using comparison tests and limit comparison test

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SUMMARY

The discussion confirms that both the limit comparison test and the standard comparison test can be used to determine the convergence of a series. Specifically, the series in question converges by the limit comparison test, but the comparison test is also deemed acceptable for this scenario. This flexibility allows for different approaches in evaluating series convergence.

PREREQUISITES
  • Understanding of series convergence concepts
  • Familiarity with the limit comparison test
  • Knowledge of the standard comparison test
  • Basic calculus principles
NEXT STEPS
  • Study the detailed mechanics of the limit comparison test
  • Explore the standard comparison test in various contexts
  • Practice solving series convergence problems using both tests
  • Review advanced topics in series convergence, such as the ratio test
USEFUL FOR

Students and educators in mathematics, particularly those focusing on calculus and series convergence, will benefit from this discussion.

Sunwoo Bae
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Homework Statement
Determine whether the following series converge or diverge by using appropriate test. (Picture below)
Relevant Equations
None
CB722E56-DDC4-4368-8164-96578AEE2EF1.jpeg

The answer sheet states that the series converges by limit comparison test (the second way).
In the case of this particular problem, would it be also okay to use the comparison test, as shown above? (The first way)

Thank you!
 
Physics news on Phys.org
Using the comparison test is fine here.
 

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