2.10.98 Number series

Condition: Examine the series for absolute and conditional convergence. In the case of convergence, find the sum of the series accurate to \(\varepsilon=0.01\). \[ \sum_{n=1}^{\infty}(-1)^{n}\left(\frac{2 n+1}{n+10}\right)^{n}, \quad \sum_{n=1}^{\infty} \frac{(-1)^{n+1} n}{(2 n) !} \]