## An Expression For e

The number e=2.718281828 is the base of the natural log.occurs in many areas of maths, and there are many methods to calculate it. One such is as the limit of the sequenceastends to infinity.

n | (1 + 1 over n)^n |

1 | 2 |

2 | 2.25 |

3 | 2.370370370 |

4 | 2.44140625 |

10 | 2.593742460 |

100 | 2.704813829 |

1000 | 2.716923932 |

10000 | 2.718145927 |

100000 | 2.718268237 |

The table shows that asgets largergets closer toWe can write

Writewhereis a fixed number.

so that as n tends to infinityThe solution to this differential equation isso putto obtain