Determine whether the following series converge or diverge. Answer "Converges" or "Diverges."

1. $\displaystyle \sum_{n=1}^{\infty} n\left(\frac{5}{3}\right)^n$

2. $\displaystyle \sum_{n=1}^{\infty}\frac{100^{n}}{n!}$

3. $\displaystyle \sum_{n=1}^{\infty}\frac{\sin 6 n}{6^n}$

Note: You only have two attempts at this problem.