Series convergence and Cauchy criterion

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SUMMARY

The discussion centers on the convergence of series and the application of the Cauchy criterion. A participant mentions selecting indices m and n such that m > n > max { N_1, N_2 }, indicating a specific approach to proving convergence. The conversation reflects a struggle with understanding the Cauchy criterion, which is essential for establishing the convergence of series in mathematical analysis.

PREREQUISITES
  • Understanding of series convergence
  • Familiarity with the Cauchy criterion
  • Knowledge of mathematical notation and indices
  • Basic concepts of limits in analysis
NEXT STEPS
  • Study the formal definition of the Cauchy criterion for series
  • Explore examples of series that converge and diverge
  • Learn about the relationship between Cauchy sequences and convergence
  • Investigate the implications of choosing indices in proofs of convergence
USEFUL FOR

Students of mathematics, particularly those studying real analysis, educators teaching series convergence, and anyone seeking to deepen their understanding of the Cauchy criterion.

estro
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The Attempt at a Solution


proof.jpg

* forgot to state that I choose m > n > max { N_1, N_2 }.

I'm not sure if i did it right, but seems ok to me =)

Will appreciate your opinion...
 
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still struggling with this one...=(
 

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