# ratio test

Let $({a}_{n})$ be a sequence of real numbers. Then the series

$$\sum _{n=1}^{\mathrm{\infty}}{a}_{n}$$ |

$$ |

and diverges if

$$\underset{n\to \mathrm{\infty}}{lim\; inf}\left|\frac{{a}_{n+1}}{{a}_{n}}\right|>1.$$ |

Title | ratio test^{} |
---|---|

Canonical name | RatioTest |

Date of creation | 2013-03-22 12:24:14 |

Last modified on | 2013-03-22 12:24:14 |

Owner | Koro (127) |

Last modified by | Koro (127) |

Numerical id | 12 |

Author | Koro (127) |

Entry type | Theorem |

Classification | msc 26A06 |

Classification | msc 40A05 |

Synonym | quotient criterion |