# Limit of a sequence

## Value to which tends an infinite sequence / From Wikipedia, the free encyclopedia

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For the general mathematical concept, see Limit (mathematics).

In mathematics, the **limit of a sequence** is the value that the terms of a sequence "tend to", and is often denoted using the $\lim$ symbol (e.g., $\lim _{n\to \infty }a_{n}$).^{[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]}

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$n$ | $n\times \sin \left({\tfrac {1}{n}}\right)$ |
---|---|

1 | 0.841471 |

2 | 0.958851 |

... | |

10 | 0.998334 |

... | |

100 | 0.999983 |

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