Cho dãy số ( u n ) thoả mãn lim n u n = 3 . Tìm giới hạn lim 2 n + 3 n 2 u n .

\(\lim \frac{{2n + 3}}{{{n^2}{u_n}}} = \lim \left( {\frac{{2n + 3}}{n} \cdot \frac{1}{{n{u_n}}}} \right) = \lim \frac{{2n + 3}}{n} \cdot \lim \frac{1}{{n{u_n}}}\)

\( = \lim \left( {2 + \frac{3}{n}} \right) \cdot \frac{1}{{\lim n{u_n}}} = 2 \cdot \frac{1}{3} = \frac{2}{3}{\rm{. }}\)