# Limit of a sequence

In mathematics, the **limit of a sequence** is the value that the terms of a sequence "tend to", and is often denoted using the symbol (e.g., ).[1] If such a limit exists, the sequence is called **convergent**.[2] A sequence that does not converge is said to be **divergent**.[3] The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests.[1]

This article needs additional citations for verification. (May 2017) |

n | n sin(1/n) |
---|---|

1 | 0.841471 |

2 | 0.958851 |

... | |

10 | 0.998334 |

... | |

100 | 0.999983 |

Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers.