Như yêu cầu . Các bạn giúp mình với ạ

Giải thích các bước giải:

 Ta có:

\(\begin{array}{l}
{C_2} = \dfrac{1}{{6.8}} + \dfrac{1}{{8.10}} + ….. + \dfrac{1}{{18.20}}\\
 = \dfrac{1}{2}.\left( {\dfrac{2}{{6.8}} + \dfrac{2}{{8.10}} + ….. + \dfrac{2}{{18.20}}} \right)\\
 = \dfrac{1}{2}.\left( {\dfrac{{8 – 6}}{{6.8}} + \dfrac{{10 – 8}}{{8.10}} + …. + \dfrac{{20 – 18}}{{18.20}}} \right)\\
 = \dfrac{1}{2}.\left[ {\left( {\dfrac{1}{6} – \dfrac{1}{8}} \right) + \left( {\dfrac{1}{8} – \dfrac{1}{{10}}} \right) + …. + \left( {\dfrac{1}{{18}} – \dfrac{1}{{20}}} \right)} \right]\\
 = \dfrac{1}{2}.\left( {\dfrac{1}{6} – \dfrac{1}{{20}}} \right)\\
 = \dfrac{1}{{12}} – \dfrac{1}{{40}} < \dfrac{1}{{12}}\\
 \Rightarrow {C_2} < \dfrac{1}{{12}}
\end{array}\)