How would you work out if these series converge or diverge?
Problem 1
n=1 to infinity n!/10^n
Problem 2
n=1 to infinity ((n-2)/n)^n
Problem 3
n=1 to infinity (-2)^n/3^n
What exactly are you having troubles with? You are already told which tests to use.
For example, the first one. Let $\displaystyle a_n = \frac{n!}{10^n}$.
Then: $\displaystyle \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n}\right| = \lim_{n \to \infty} \left| \frac{(n+1)!}{10^{n+1}} \cdot \frac{10^n}{n!}\right| = \lim_{n \to \infty} \left|\frac{(n+1)n!}{10^n \cdot 10} \cdot \frac{10^n}{n!}\right| = \cdots$