Giới hạn \(\lim \frac{{{{12}^n} - {{11}^n}}}{{{4^n} + {{4.12}^n} + 3}}\) bằng

* Hướng dẫn giải

Ta có: \(\lim \frac{{{{12}^n} - {{11}^n}}}{{{4^n} + {{4.12}^n} + 3}}\)\( = \lim \frac{{1 - {{\left( {\frac{{11}}{{12}}} \right)}^n}}}{{{{\left( {\frac{1}{3}} \right)}^n} + 4 + \frac{3}{{{{12}^n}}}}}\) \( = \frac{{1 - 0}}{{0 + 4 + 0}} = \frac{1}{4}\).