Question

Tính nhanh nếu có thể

1. \(\dfrac{-1}{24}-[\dfrac{1}{4}-\left(\dfrac{1}{2}-\dfrac{7}{8}\right)]\)

2. \((\dfrac{5}{7}-\dfrac{7}{5})-[\dfrac{1}{2}-(-\dfrac{2}{7}-\dfrac{1}{10})]\)

3.\(\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}+\dfrac{1}{7\cdot9}+.......+\dfrac{1}{2015\cdot2017}\)

Answer 1

3.đặt biểu thức trên là A

ta có:

2A=2.(\(\dfrac{1}{3.5}\)+\(\dfrac{1}{5.7}\)+\(\dfrac{1}{7.9}\)+...+\(\dfrac{1}{2015.2017}\))

=>2A=\(\dfrac{2}{3.5}\)+\(\dfrac{2}{5.7}\)+\(\dfrac{2}{7.9}\)+....+\(\dfrac{2}{2015.2017}\)

=>2A=\(\dfrac{1}{3}\)-\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\)-\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\)-\(\dfrac{1}{9}\)+....\(\dfrac{1}{2015}\)-\(\dfrac{1}{2017}\)

=>2A=\(\dfrac{1}{3}\)-\(\dfrac{1}{2017}\)=\(\dfrac{2014}{6051}\)

=>A=\(\dfrac{2014}{6051}\):2=\(\dfrac{1007}{6051}\)