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