# bounds for e

Taking the limit as $n\to \mathrm{\infty}$, we obtain an upper bound^{} for $e$.
Combining this with the fact that the ${(1+1/n)}^{n}$ is an increasing
sequence, we have the following bounds for $e$:

$$ |

This can be used to show that $e$ is not an integer – if we take $m=5$, we obtain $$, for instance.

Title | bounds for e |
---|---|

Canonical name | BoundsForE |

Date of creation | 2013-03-22 15:48:48 |

Last modified on | 2013-03-22 15:48:48 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 7 |

Author | rspuzio (6075) |

Entry type | Theorem |

Classification | msc 33B99 |