Answer
$$0$$
Work Step by Step
$\lim\limits_{n \to \infty} (n-\sqrt {n^2-1})=\lim\limits_{n \to \infty} (n-\sqrt {n^2-1}) \times \dfrac{ (n+\sqrt {n^2-1})}{ (n+\sqrt {n^2-1})}\\=\lim\limits_{n \to \infty} \dfrac{ 1}{ (n+\sqrt {n^2-1})}\\=\dfrac{1}{\infty}\\=0$
