I got me finals tomorrow. Proving the divergence of the Harmonic Series

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SUMMARY

The discussion centers on the divergence of the Harmonic Series and the validity of using the Integral Test as a proof method. Participants confirm that the Integral Test is applicable if the series meets its requirements, which include being positive, continuous, and decreasing. The conversation highlights the preference for simpler proofs over lengthy term listings, emphasizing the importance of understanding the underlying principles rather than merely following procedural steps.

PREREQUISITES
  • Understanding of the Harmonic Series
  • Familiarity with the Integral Test for convergence
  • Knowledge of series convergence criteria
  • Basic proof techniques in mathematics
NEXT STEPS
  • Study the requirements for the Integral Test in detail
  • Explore alternative proofs for the divergence of the Harmonic Series
  • Learn about other convergence tests, such as the Comparison Test
  • Practice grouping terms in series to simplify proofs
USEFUL FOR

Students preparing for mathematics finals, particularly those studying series and convergence, as well as educators looking for effective proof strategies in calculus.

flyingpig
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Homework Statement



My professor warned us that a few proofs will be on the finals. This could be one of them.

However, we did a proof in class where he listed out a bunch of terms and then did an inequality to say it is divergent.

I personally hated that long proof. I don't want to bother writing out 50 terms just to prove this.

Now my question is, in Math, am I allowed to "prove" the Harmonic Series is divergent using a series test? Such as the Integral test?
 
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Why not? The integral test is a valid test if you prove the series meets the requirements of the integral test. What are they? If you don't have that, a more elementary proof doesn't involve writing out 50 terms. It just involves thinking and grouping the terms. Why this whining about it?
 
I used to have some problems with proofs because I had trouble with a "particular case" and a "general case". I just wasn't **** about this one lol. Thanks anyways!
 

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