lim n → + ∞ n + 1/ 3 n bằng

Đáp án đúng là: D

Ta có: \(\mathop {\lim }\limits_{n \to + \infty } \frac{{n + 1}}{{3n}} = \mathop {\lim }\limits_{n \to + \infty } \frac{{1 + \frac{1}{n}}}{3} = \frac{{\mathop {\lim }\limits_{n \to + \infty } \left( {1 + \frac{1}{n}} \right)}}{{\mathop {\lim }\limits_{n \to + \infty } 3}} = \frac{{\mathop {\lim }\limits_{n \to + \infty } 1 + \mathop {\lim }\limits_{n \to + \infty } \frac{1}{n}}}{{\mathop {\lim }\limits_{n \to + \infty } 3}} = \frac{{1 + 0}}{3} = \frac{1}{3}.\)