Leibniz Criterion

analysis

Definition

Leibniz Criterion

According to the Leibniz criterion, an alternating series ${\sum }_{n\ge 0}(-1{)}^n{a}_n$ with $a_n$ being monotonously decreasing and ${\lim }_{n\to \infty }{a}_n=0$ ($a_n$ being a zero sequence) implies that the series is convergent.

Note that this is not a classical criterion as common in mathematics since the implication does only apply in one direction.