Theory

Theory 1

Simple Divergence Test (SDT)

Applicability: Any series.

Test Statement:

$$\underset{n\to \infty }{\lim }{a}_n\ne 0⟹\sum _{n=1}^{\infty }{a}_n\text{diverges}$$

AKA the “Not Even Close” test

The converse is not valid. For example, ${\sum }_{n=1}^{\infty }\frac{1}{n}$ diverges even though ${\lim }_{n\to \infty }\frac{1}{n}=0$.