Definition:Alternating Series

Definition

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

The series $s$ is an alternating series if and only if the terms of $\sequence {a_n}$ alternate between positive and negative.

Also see

• Results about alternating series can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): alternating series
• 1992: Larry C. Andrews: Special Functions of Mathematics for Engineers (2nd ed.) ... (previous) ... (next): $\S 1.2.2$: Summary of convergence tests
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): alternating series
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): alternating series
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): alternating series