5.11 Comparison & limit comparison test
Comparison & limit comparison test
Lessons
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.

1.
Overview:

2.
Convergence & Divergence of Comparison Tests
Use the Comparison Test to determine if the series converge or diverge. 
3.
Convergence & Divergence of Limit Comparison Tests
Use the Limit Comparison Test to determine if the series converge or diverge.