Ta có:
Đặt \(A=\)\(\dfrac{1}{4.7}+\dfrac{1}{7.10}+\dfrac{1}{10.13}+...+\dfrac{1}{604.607}< \dfrac{1}{2}\)
\(=\dfrac{1}{3}.\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+...+\dfrac{1}{604}-\dfrac{1}{607}\right)< \dfrac{1}{2}\)
\(=\dfrac{1}{3}.\left(\dfrac{1}{4}-\dfrac{1}{607}\right)< \dfrac{1}{2}\)
Vì \(\dfrac{1}{3}< \dfrac{1}{2}\) nên \(\dfrac{1}{3}.\left(\dfrac{1}{4}-\dfrac{1}{607}\right)< \dfrac{1}{2}\)
Vậy \(A< \dfrac{1}{2}\)
............................... =) A < 1/2