Câu 5 : Tính nhanh 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ... + 1/37.38.39

$\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{37.38.39}$

$=(\dfrac{2}{1.2.3}+\dfrac{2}{234}+\dfrac{2}{3.4.5}+...+\dfrac{2}{37.38.39}):2$

$=(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{37.38}-\dfrac{1}{38.39}):2$

$=(\dfrac{1}{2}-\dfrac{1}{38.39}):2$

$=(\dfrac{1}{2}-\dfrac{1}{1482}):2$

$=\dfrac{370}{741}:2$

$=\dfrac{370}{1482}$

$=\dfrac{185}{741}$