Limit Comparison Test: Does Order Matter?

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SUMMARY

The Limit Comparison Test in calculus establishes that the order of functions in the ratio does not affect the outcome of the test. Specifically, when comparing two positive sequences, the limit of the ratio of the smaller sequence to the larger sequence should be evaluated. This confirms that the convergence or divergence of the series remains consistent regardless of the arrangement of the functions in the ratio.

PREREQUISITES
  • Understanding of sequences and series in calculus
  • Familiarity with the Limit Comparison Test
  • Knowledge of convergence and divergence concepts
  • Basic proof techniques in mathematical analysis
NEXT STEPS
  • Study the formal proof of the Limit Comparison Test
  • Explore examples of applying the Limit Comparison Test with different sequences
  • Learn about other comparison tests for series convergence
  • Investigate the implications of the ratio test in series analysis
USEFUL FOR

Students of calculus, mathematics educators, and anyone studying series convergence in advanced mathematics.

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I was just wondering for the limit comparison test does it matter which function is on the top and bottom?
 
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I haven't verified this yet, but doing a rough sketch of the proof, it seems to me that the 'smaller' sequence needs to be the ratio on top.
 

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