Tìm lim ( 3 n − 1 n .2 n + 2024 ) .

\(\lim \left( {\frac{{3n - 1}}{{n{{.2}^n}}} + 2024} \right)\)\( = \lim \left( {\frac{{3 - \frac{1}{n}}}{{{2^n}}} + 2024} \right)\).

Vì \(\lim \left( {3 - \frac{1}{n}} \right) = 3;\lim {2^n} =  + \infty \) nên \(\lim \frac{{3 - \frac{1}{n}}}{{{2^n}}} = 0\).

Vậy \(\lim \left( {\frac{{3n - 1}}{{n{{.2}^n}}} + 2024} \right) = 2024\).

Trả lời: 2024.