Ta có : \(\left\{{}\begin{matrix}\dfrac{1}{14}< \dfrac{1}{10}\\\dfrac{1}{23}< \dfrac{1}{10}\end{matrix}\right.\)
\(\Rightarrow\dfrac{1}{14}+\dfrac{1}{23}< \dfrac{1}{10}+\dfrac{1}{10}=\dfrac{1}{5}\)
Lại có : \(\left\{{}\begin{matrix}\dfrac{1}{62}< \dfrac{1}{60}\\\dfrac{1}{83}< \dfrac{1}{60}\\\dfrac{1}{117}< \dfrac{1}{60}\end{matrix}\right.\)
\(\Rightarrow\dfrac{1}{62}+\dfrac{1}{83}+\dfrac{1}{117}< \dfrac{1}{60}+\dfrac{1}{60}+\dfrac{1}{60}=\dfrac{1}{20}\)
\(\Rightarrow\dfrac{1}{5}+\dfrac{1}{14}+\dfrac{1}{23}+\dfrac{1}{62}+\dfrac{1}{83}+\dfrac{1}{117}< \dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{20}=\dfrac{9}{20}< \dfrac{10}{20}=\dfrac{1}{2}\)
