# alternating series

An *alternating series ^{}* is a series of the form

$$\sum _{i=0}^{\mathrm{\infty}}{(-1)}^{i}{a}_{i}$$ |

or

$$\sum _{i=0}^{\mathrm{\infty}}{(-1)}^{i+1}{a}_{i}$$ |

where $({a}_{n})$ is a non-negative sequence. Loosely, this is just a series where the “alternate” between positive and negative.

For convergence issues, see the following entry: alternating series test^{} (http://planetmath.org/AlternatingSeriesTest).

Title | alternating series |
---|---|

Canonical name | AlternatingSeries |

Date of creation | 2013-03-22 12:27:05 |

Last modified on | 2013-03-22 12:27:05 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 6 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 40-00 |

Synonym | alternating series test |

Related topic | LeibnizsTheorem |

Related topic | ProofOfLeibnizsTheorem |

Related topic | AlternatingSeriesTest |