MHB How Do I Correctly Apply the Alternating Series Test?

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The discussion revolves around applying the Alternating Series Test to a specific series. The user has attempted to solve a problem but received rejection from the system without clear feedback. They provided a series example for further clarification. Participants are encouraged to assist with the application of the test and the reasoning behind the rejection of the initial answers. The conversation highlights the need for understanding the criteria of the Alternating Series Test in evaluating convergence.
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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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