Giá trị của \(C = \lim {2{n^2} + 1} {n + 2} + 1}}\) bằng:

* Hướng dẫn giải

\(\begin{array}{l}
C = \lim \;\frac{{{{\left( {2{n^2} + 1} \right)}^4}{{\left( {n + 2} \right)}^9}}}{{{n^{17}} + 1}} = \lim \frac{{{n^8}{{\left( {2 + \frac{1}{{{n^2}}}} \right)}^4}.{n^9}{{\left( {1 + \frac{2}{n}} \right)}^9}}}{{{n^{17}}\left( {1 + \frac{1}{{{n^{17}}}}} \right)}}\\
 = \lim \frac{{\left( {2 + \frac{1}{{{n^4}}}} \right){{\left( {1 + \frac{2}{n}} \right)}^9}}}{{1 + \frac{1}{{{n^{17}}}}}} = \frac{{{{\left( {2 + 0} \right)}^4}.{{\left( {1 + 0} \right)}^9}}}{{1 + 0}} = 16
\end{array}\)