Definition:Positive Series

Definition

Let $\ds s = \sum_{n \mathop = 1}^\infty a_n$ be a series in the real numbers $\R$.

The series $s$ is a positive series if and only if either:

$\forall n \in \N: a_n > 0$

or:

$\forall n \in \N: a_n < 0$

That is, if all terms of $\sequence {a_n}$ are either all (strictly) positive or (strictly) negative.

Also defined as

Some sources define a positive series as exclusively a series whose terms are all (strictly) positive.

Sources

• 1992: Larry C. Andrews: Special Functions of Mathematics for Engineers (2nd ed.) ... (previous) ... (next): $\S 1.2.2$: Summary of convergence tests
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): positive series