2.10.100 Number series

Condition: Investigate the convergence of number series: 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 convergence. a) \( \sum_{n=1}^{\infty} \frac{\pi^{n}}{3^{n} \cdot n^{3}} \), b) \( \sum_{n=1}^{\infty} \frac{\sin n}{5^{n}}\).