When learning about infinite series, there are a few important tests that can help us understand if they will "converge" or "diverge".

Here are three ways to check:

1. The Comparison Test: This test helps you compare your series to a known series. If the known series converges, your series might converge too.

2. The Ratio Test: For this test, you look at how the terms in the series relate to each other. You find a limit, which we call $L$, by using this formula: $L = \lim_{n \to \infty} \frac{a_{n+1}}{a_n}$. If $L$ is less than 1, then your series converges!

3. The Root Test: This one checks the roots of the terms in your series. You find a limit here as well: $L = \lim_{n \to \infty} \sqrt[n]{|a_n|}$. Again, if $L$ is less than 1, then your series converges.

By learning and practicing these tests, figuring out infinite series becomes much simpler!