Tính lim n → + ∞ ( √ n 2 + 3 n − n ) .

\(\mathop {\lim }\limits_{n \to + \infty } \left( {\sqrt {{n^2} + 3n} - n} \right)\)\( = \mathop {\lim }\limits_{n \to + \infty } \frac{{{n^2} + 3n - {n^2}}}{{\sqrt {{n^2} + 3n} + n}}\)\( = \mathop {\lim }\limits_{n \to + \infty } \frac{{3n}}{{n\left( {\sqrt {1 + \frac{3}{n}} + 1} \right)}} = \frac{3}{2} = 1,5\).

Trả lời: 1,5.