analysis - Determine whether this series is absolutely convergent, conditionally convergent or divergent?

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 $\sum \frac{1}{n+1}$