# Convergence of $\sum \limits_{k=1}^\infty (\frac{k^3}{-1-k^4})$

How to prove con/di vergence of $\sum \limits_{k=1}^\infty (\frac{k^3}{-1-k^4})=\sum \limits_{k=1}^\infty -(\frac{k^3}{k^4+1})$
My problem is that I don't know how to do that I tried some different methodes but it doesn't work.Does anyone have an idea?Can I prove it by the p-test although there is a (-1)?

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Another way: $$\sum_{k=1}^{\infty}\frac{1}{2k}\leq\sum_{k=1}^{\infty}\frac{1}{k+\frac{1}{k}}=\sum_{k=1}^{\infty}\frac{k^3}{k^4+1}$$
This follows from the fact that $\forall k\in Z^+[2k\geq k+\frac{1}{k}]$