Definition:Oscillating Series

Definition

An oscillating series is a divergent series which is not properly divergent.

Examples

Arbitrary Example

This series:

$1 - 2 + 3 - 4 + \cdots$

is an example of an oscillating series.

Grandi's Series

Grandi's series:

$\ds \sum_{n \mathop = 0}^\infty \paren {-1}^n$

is an example of an oscillating series.

Also see

• Definition:Properly Divergent Series

• Results about oscillating series can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): divergent series
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): oscillating series (oscillating divergent series
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): divergent series
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): oscillating series (oscillating divergent series