How Do I Correctly Apply the Alternating Series Test?

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    Convergence Series
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SUMMARY

The discussion focuses on the application of the Alternating Series Test to the series $$\sum_{n=1}^\infty (-1)^n \left( \frac{3n-1}{n^2} \right)^n$$. Participants share their attempts at solving the problem, with one user reporting answers of 4, 8, 9, and 10, which were subsequently rejected by the system. The conversation highlights the need for clarity in applying the test and understanding the conditions that must be met for convergence.

PREREQUISITES
  • Understanding of the Alternating Series Test
  • Familiarity with convergence criteria for infinite series
  • Basic knowledge of mathematical notation and series
  • Ability to manipulate and simplify algebraic expressions
NEXT STEPS
  • Review the conditions for convergence in the Alternating Series Test
  • Practice applying the Alternating Series Test to various series
  • Explore examples of series that fail the Alternating Series Test
  • Learn about other convergence tests, such as the Ratio Test and Root Test
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to deepen their understanding of series convergence, particularly through the Alternating Series Test.

chrisgoodie
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View attachment 5930

Hi guys, I am doing this question of alternating series test.

And I was following the below principles when solving the problem. Sorry I don't know how to type in the math language. I got 4, 8, 9, 10 as the answers. But the system rejected this without any explanation. Can someone throw a lifeline?

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Hey chrisgoodie! Welcome to MHB! ;)

How about this one:
$$\sum_{n=1}^\infty (-1)^n \left( \frac{3n-1}{n^2} \right)^n$$
(Wondering)
 

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