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 | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

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

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

# Converging to a limit

**Physics Forums | Science Articles, Homework Help, Discussion**