Giải thích các bước giải:
Câu 13:
\(\begin{array}{l}
\frac{1}{{n\left( {n + 1} \right)}} = \frac{{\left( {n + 1} \right) - n}}{{n\left( {n + 1} \right)}} = \frac{1}{n} - \frac{1}{{n + 1}}\\
\lim \left( {1 + \frac{1}{{1.2}} + \frac{1}{{2.3}} + .... + \frac{1}{{n\left( {n + 1} \right)}}} \right)\\
= \lim \left( {1 + 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + .... + \frac{1}{n} - \frac{1}{{n + 1}}} \right)\\
= \lim \left( {2 - \frac{1}{{n + 1}}} \right)\\
\lim \frac{1}{{n + 1}} = 0 \Rightarrow \lim \left( {2 - \frac{1}{{n + 1}}} \right) = 2
\end{array}\)
Câu 14:
\(\begin{array}{l}
\lim {u_n} = 2\\
\Leftrightarrow \lim \frac{{4{n^2} + 5n + 2}}{{a{n^2} + 2017}} = 2\\
\Leftrightarrow \lim \frac{{4 + \frac{5}{n} + \frac{2}{{{n^2}}}}}{{a + \frac{{2017}}{{{n^2}}}}} = 2\\
\Leftrightarrow \frac{4}{a} = 2\\
\Leftrightarrow a = 2
\end{array}\)
