The series $ \sum_{n=1}^{\infty} \frac{(-1)^n n}{n^2 + 1} $; is it absolutely convergent, conditionally convergent or divergent?
This question is meant to be worth quite a few marks so although I thought I had the answer using the comparison test, I think I'm supposed to incorporate the alternating series test.
Answer
Your series is convergent by Leibniz-theorem but not absolutely convergent as you can see by comparison with $\sum \frac{1}{n+1}$
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