Comparison & limit comparison test

Notes:

Note *The Comparison test says the following:
Let $\sum a_n$ and $\sum b_n$ be two series where $a_n\leq b_n$ for all $n$ and $a_nb_n\geq0$. Then we say that
1. If $\sum b_n$ is convergent, then $\sum a_n$ is also convergent
2. If $\sum a_n$ is divergent, then $\sum b_n$ is also divergent.

The Limit Comparison Test says the following:
Let $\sum a_n$ and $\sum b_n$ be two series where $a_n\geq 0$ and $b_n$ > 0 for all $n$. Then we say that

$\lim$_{n →$\infty$} $\frac{a_n}{b_n}=c$

If $c$ is a positive finite number, then either both series converge or diverge.