2.10.112 Number series

Condition: Examine the series for convergence: 1) \( \sum_{n=1}^{\infty} \frac{3 n}{5 n+1} \), 2) \( \sum_{n=1}^{\infty} \frac{(n+1)^{2}}{n^{4}+2 n^{2}+1} \) 3) \( \sum_{n=1}^{\infty} \tan \frac{1}{\sqrt{n}} \)