The Ratio Test

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

The Ratio Test

Assume that the following limit exists (or $=\infty$): $L={\lim }_{k\to \infty }\left|\frac{a_{k+1}}{a_k}\right|$

• 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.