I managed to get this series to converge but I have no idea whether it will converge absolutely.Does the sequence $\displaystyle \sum_{n=1}^\infty \frac{sin(2n)}{1+n+n^2}$ converge? If it does, does it converge absolutely?

I gather that there will no longer be any positive terms but I can't prove whether it is absolutely convergent or not.

Help would be appreciated!