Does the series $\displaystyle {\sum_{{{k}={1}}}^{{\infty}}}\ \frac{{\cos{{\left(\frac{{1}}{{k}}\right)}}}}{{\sqrt[{{9}}]{{{k}^{{2}}+{3}}}}}$ converge absolutely, converge conditionally or diverge?

Does the series $\displaystyle {\sum_{{{k}={1}}}^{{\infty}}}\ \frac{{\cos{{\left({k}\pi\right)}}}}{{\sqrt[{{9}}]{{{k}^{{2}}+{3}}}}}$ converge absolutely, converge conditionally or diverge?