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.