Giải thích các bước giải:
\(\begin{array}{l}
a,\\
\lim \frac{{2n + 1}}{{3n + 2}} = \lim \frac{{2 + \frac{1}{n}}}{{3 + \frac{2}{n}}} = \frac{{2 + 0}}{{3 + 0}} = \frac{2}{3}\\
b,\\
\lim \frac{{n! + \left( {n + 1} \right)!}}{{2\left( {n + 1} \right)! + 7n!}}\\
= \lim \frac{{n! + \left( {n + 1} \right).n!}}{{2.\left( {n + 1} \right).n! + 7n!}}\\
= \lim \frac{{n!.\left[ {1 + \left( {n + 1} \right)} \right]}}{{n!.\left[ {2\left( {n + 1} \right) + 7} \right]}}\\
= \lim \frac{{n + 2}}{{2n + 9}}\\
= \lim \frac{{1 + \frac{2}{n}}}{{2 + \frac{9}{n}}}\\
= \frac{1}{2}
\end{array}\)
