# How to find this limit?

• February 5th 2009, 02:41 PM
ninano1205
How to find this limit?
lim((n-1)/n)^n,n->+inf)
calculator gives me e^-1 bt I don't know how.
• February 5th 2009, 02:51 PM
ThePerfectHacker
Quote:

Originally Posted by ninano1205
lim((n-1)/n)^n,n->+inf)
calculator gives me e^-1 bt I don't know how.
Notice that $\tfrac{n-1}{n} = 1 - \tfrac{1}{n}$.
You should know that $\left( 1 + \tfrac{1}{n} \right)^n \to e$, in general $\left( 1+\tfrac{k}{n} \right)^n \to e^k$.
Therefore, $\left( 1 - \tfrac{1}{n} \right)^n \to e^{-1}$.