2.10.22 Number series

Problem: Examine the convergence of the series. 1) \( \sum_{n=1}^{\infty}\left(1-\cos \frac{1}{\sqrt{n}}\right) \), 2) \( \sum_{n=1}^{\infty}(-1)^{n+1} \cdot\left(\frac{3 n}{3 n+1}\right)^{n^{2}} \).