Đặt $A = \dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+.....+\dfrac{1}{37.38.39}$
$\to 2A =\dfrac{2}{1.2.3}+\dfrac{2}{2.3.4}+.....+\dfrac{2}{37.38.39}$
$\to 2A = \dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+....+\dfrac{1}{37.38}-\dfrac{1}{38.39}$
$\to 2A = \dfrac{1}{1.2}-\dfrac{1}{38.39} =\dfrac{370}{741}$
$\to A = \dfrac{185}{741}$