I am asked to find the following series $$\sum_{k=1}^{\infty}\frac{(-1)^{k + 1} k^2}{k^3 + 1}$$ I know this converges via the alternating series test since $$\lim_{k\rightarrow\infty}\frac{k^2}{k^3 + 1}=0$$ and $\frac{k^2}{k^3 + 1}$ is strictly decreasing.
However, I have 0 clue as to how to evaluate this.
