Is the Alternating Series Convergent? Tips and Tricks for Solving

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The discussion centers on determining the convergence of the alternating series Sum(((-1)^(n-1)) * ((2n+1)/(n+2))) from 1 to infinity. The alternating series test requires both that the limit of the terms approaches zero and that the terms are monotonically decreasing; however, the limit does not approach zero, indicating divergence. Participants debate the implications of necessary and sufficient conditions for convergence, with some arguing that failing one condition means the series cannot converge. Additionally, there are side discussions about finding the radius of convergence for other series, ultimately concluding that the radius is zero for one of them. The conversation highlights the complexities of convergence tests and the importance of understanding mathematical logic.
  • #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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