2.10.101 Number series

Condition: a) Find out whether the positive series converges or diverges. b) Find out whether the alternating series converges or diverges; if the series converges, establish the nature of the convergence. a) \( \sum_{n=1}^{\infty} \arcsin \left(\frac{3}{4}\right)^{n} \), b) \( \sum_{n=1}^{\infty} \frac{(-1)^{n}(5 n-2)}{n \sqrt{25 n^{2}+1}} \).