Tính lim n → + ∞ ( √ n 2 − n − √ n 2 + 1 )

\(\mathop {\lim }\limits_{n \to + \infty } \left( {\sqrt {{n^2} - n} - \sqrt {{n^2} + 1} } \right) = \mathop {\lim }\limits_{n \to + \infty } \frac{{ - n - 1}}{{\sqrt {{n^2} - n} + \sqrt {{n^2} + 1} }} = \mathop {\lim }\limits_{n \to + \infty } \frac{{ - 1 - \frac{1}{n}}}{{\sqrt {1 - \frac{1}{n}} + \sqrt {1 + \frac{1}{{{n^2}}}} }} = - \frac{1}{2}\)