the result of the above mentioned limit is infinity minus infinity = zero, or do you calculate it differently?
$\displaystyle \lim_{n \to \infty }\sqrt{n}-\sqrt{n-1}=\lim_{n \to \infty }(\sqrt{n}-\sqrt{n-1})\cdot \frac{\sqrt{n}+\sqrt{n-1}}{\sqrt{n}+\sqrt{n-1}}=\lim_{n \to \infty }\frac{1}{\sqrt{n}+\sqrt{n-1}}=0$