[tex] \lim_{n \to \infty} ( \frac{n}{n-2} )^{n}[/tex]

[tex]lim_{x\to +\infty}(\frac{n}{n-2})^{n}=lim(1+\frac{2}{n-2})^{\frac{n-2}{2}\cdot \frac{2n}{n-2}}=lime^{\frac{2n}{n-2}}=\\\\=e^{lim\frac{2n}{n-2}}=e^2[/tex]