Math Challenges

Submissions for Problem #84

Explain why the following series converges or diverges.

\[ \sum_{n=1}^{\infty}\left(-1\right)^{n+1}\frac{2+n}{n^2} \]

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Solution: \( \lim_{n\to\infty}\frac{2+n}{n^2}=0\text{ and the sequence is alternating} \)

Explanation:
Convergent by the Alternating Series Test