2.10.120 Number series

condition: Examine the series for convergence: 1) \( \sum_{\mathrm{H} 1}^{\infty}\left(\frac{2 n^{2}+1}{n^{2}+1}\right)^{n^{2}} \), 2) \( \sum_{n=2}^{\infty} \frac{(-1)^{n+1}}{\ln (n+1)} \).