Đáp án:
$\begin{array}{l}
4)\lim \frac{{{2^n} + {5^{n + 1}}}}{{1 + {5^n}}} = \lim \frac{{\frac{{{2^n}}}{{{5^n}}} + 5}}{{\frac{1}{{{5^n}}} + 1}} = 5\\
5)\lim \frac{{1 - {{2.3}^n} + {6^n}}}{{{2^n}\left( {{3^{n + 1}} - 5} \right)}} = \lim \frac{{1 - {{2.3}^n} + {6^n}}}{{{{3.6}^n} - {{5.2}^n}}} = \lim \frac{{\frac{1}{{{6^n}}} - 2.\frac{{{3^n}}}{{{6^n}}} + 1}}{{3 - 5.\frac{{{2^n}}}{{{6^n}}}}} = \frac{1}{3}\\
6)\lim \frac{{1 + {{2.3}^n} - {7^n}}}{{{5^n} + {{2.7}^n}}} = \lim \frac{{\frac{1}{{{7^n}}} + 2.\frac{{{3^n}}}{{{7^n}}} - 1}}{{\frac{{{5^n}}}{{{7^n}}} + 2}} = - \frac{1}{2}
\end{array}$
