2.10.131 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) \( \sum_{n=1}^{\infty} \frac{\sin ^{2} n}{n^{2}+1} \) 2) \( \sum_{n=1}^{\infty} \frac{1}{\sqrt[3]{n}+2} \arctan \frac{n+3}{n^{2}+5} \).