Gọi \(A=\dfrac{1}{4}+\left(\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{9}\right)+\left(\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{19}\right)\)
Vì \(\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{9}>\dfrac{1}{9}+\dfrac{1}{9}+...+\dfrac{1}{9}\) nên \(\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{9}>\dfrac{5}{9}>\dfrac{1}{2}\).
Vì \(\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{19}>\dfrac{1}{19}+\dfrac{1}{19}+...+\dfrac{1}{19}\) nên \(\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{19}>\dfrac{10}{19}>\dfrac{1}{2}\).
\(\Rightarrow A>\dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{2}>1\)
\(\Rightarrow A>1\)