MHB How Do I Correctly Apply the Alternating Series Test?

[chrisgoodie]

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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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[I like Serena]

Hey chrisgoodie! Welcome to MHB! ;)

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