How do you prove that the lim n->infinity (n-1/n)=1?(adsbygoogle = window.adsbygoogle || []).push({});

I know that the definition of convergence for a sequence xn is for all E>0, there exists an N is an element of the set of a natural numbers and there exists a n>=N, such that lxn-Ll<E.

Is it sufficient to just show that 1 is the least upper bound, and that

1- (n-1/n) <E and thus 1-E<(n-1/n) and then n-nE<n-1 and ultimately there is an n such that n-nE+1<n

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Converging to a limit

Loading...

Similar Threads - Converging limit | Date |
---|---|

I Cauchy's Integral Test for Convergence | Jun 20, 2016 |

Convergence of improper integrals | Jun 8, 2015 |

Convergent limits for sequences: please help picture terms | Jan 26, 2014 |

Limit proof on Sequence Convergence | Apr 29, 2012 |

Can two different infinite series converge to the same limit? | Dec 27, 2011 |

**Physics Forums - The Fusion of Science and Community**