The Ratio Test

Made this it’s own, see Power Series because it is useful for the radius of convergence.

title: [[The Ratio Test]]
Assume that the following limit exists (or $= \infty$):
$$L = \lim_{k \to \infty} \Big\vert \frac{a_{k+1}}{a_k}\Big\vert$$
 
- If $L < 1$, then $\sum a_k$ is absolutely convergent.
- If $L > 1$, then $\sum a_k$ is divergent.
- If $L = 1$, then the test fails.