. Test the series for convergence or divergence. \text { a) } \sum_{n=1}^{\infty}\left(\frac{5 n^{2}-3 n+1}{3 n^{2}+4}\right)^{n} \text { b) } \sum_{n=1}^{\infty} \frac{(-1)^{n}(n+2)}{2 n^{2}+1}