Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{C_2} = \dfrac{1}{{6.8}} + \dfrac{1}{{8.10}} + ..... + \dfrac{1}{{18.20}}\\
= \dfrac{1}{2}.\left( {\dfrac{2}{{6.8}} + \dfrac{2}{{8.10}} + ..... + \dfrac{2}{{18.20}}} \right)\\
= \dfrac{1}{2}.\left( {\dfrac{{8 - 6}}{{6.8}} + \dfrac{{10 - 8}}{{8.10}} + .... + \dfrac{{20 - 18}}{{18.20}}} \right)\\
= \dfrac{1}{2}.\left[ {\left( {\dfrac{1}{6} - \dfrac{1}{8}} \right) + \left( {\dfrac{1}{8} - \dfrac{1}{{10}}} \right) + .... + \left( {\dfrac{1}{{18}} - \dfrac{1}{{20}}} \right)} \right]\\
= \dfrac{1}{2}.\left( {\dfrac{1}{6} - \dfrac{1}{{20}}} \right)\\
= \dfrac{1}{{12}} - \dfrac{1}{{40}} < \dfrac{1}{{12}}\\
\Rightarrow {C_2} < \dfrac{1}{{12}}
\end{array}\)
