Is the Alternating Series Convergent? Tips and Tricks for Solving

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SUMMARY

The discussion centers on the convergence of the alternating series defined by the sum Σ((-1)^(n-1) * (2n+1)/(n+2)) from 1 to infinity. Participants conclude that the series does not converge because the limit of a_n as n approaches infinity is 2, which fails the necessary condition for convergence in the alternating series test. The series is deemed divergent as neither criterion of the alternating series test is satisfied. Furthermore, the conversation touches on the radius of convergence for two power series, with the first yielding a radius of 1 and the second a radius of 1/2.

PREREQUISITES
  • Understanding of the Alternating Series Test
  • Familiarity with limits and monotonic sequences
  • Knowledge of power series and their convergence
  • Basic proficiency in mathematical logic and proofs
NEXT STEPS
  • Study the Alternating Series Test in detail
  • Learn about necessary and sufficient conditions for convergence
  • Explore the concept of radius of convergence for power series
  • Investigate advanced convergence tests such as Abel and Cesàro summation
USEFUL FOR

Students preparing for calculus exams, mathematicians interested in series convergence, and educators teaching series and sequences in mathematics.

  • #31
;)

Well, We all have our 'I need help' problems, it is just a matter of practice and becoming every day a little bit more masochist and stubborn in order to solve them LOL (I'm stuck on one of those now). And because of that, it is nice to have the help and hints when are needed.

Good Luck, in your examination!
 
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