Confirming an Inequality: Seeking Help

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SUMMARY

The discussion centers on the application of the comparison test in analyzing series convergence. The user seeks confirmation regarding the limit of b-subn equaling 0, which renders the comparison test inconclusive. Additionally, the user asserts that their simplified form of a-subn is valid and that their inequality holds true, despite the series diverging for large n, where the terms approximate 1/n.

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  • Understanding of series convergence tests, specifically the comparison test.
  • Familiarity with limits and their implications in series analysis.
  • Knowledge of divergent series, particularly those resembling harmonic series.
  • Basic mathematical notation and terminology related to sequences and series.
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  • Study the formal definition and application of the comparison test in series convergence.
  • Explore the implications of limits in series analysis, focusing on cases where limits equal 0.
  • Learn about divergent series and their characteristics, particularly the harmonic series.
  • Review mathematical proofs related to inequalities in series convergence.
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Mathematicians, students studying calculus or real analysis, and anyone interested in series convergence and divergence analysis.

Square1
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Hey check out the attached picture. I think I solved the issue now but just to confirm perhaps...

If I were to continue here using the comparison test, is the only problem that b-subn limit equals 0, so the comparison test is inconclusive?

Otherwise, since our summation does not included n=0 (or other undefined values right?), my simplified form of a-subn holds, and my inequality is correct?

Thanks for any help.
 

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Your picture is hard to read. However, it seems you have a series where for large n, the terms are approximately 1/n, so the series diverges.
 

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