2.10.132 Number series

condition: Examine the series for convergence, illustrate the fact of convergence or divergence of the series by constructing a graph of the sequence of its partial sums. 1) \( \sum_{n=1}^{\infty}\left(\frac{n+2}{3 n-1}\right)^{n^{2}} \); 2) \( \sum_{n=4}^{\infty} \frac{1}{(3 n-1) \sqrt{\ln (n-2)}} \).