Alternating Series Test

Last updated Jan 17, 2022 Edit Source

• Math analysis
• Math calculus

An alternating series is basically a series whose terms’ signs are changing regularly. They often have the form

$$ \sum_{n=1}^\infty (-1)^n a_n $$

in order for such a series to converge, it needs to satisfy all three of the requirements below:

1. It is alternating.
2. $|a_{n+1}| < |a_n|$ for all $n$
3. $\lim_{n\to\infty} a_n = 0$