Question

Bài 5 (0,5 điểm) : Tính giá trị của biểu thức:

Answer 1

Ta có: \(A=\dfrac{2019}{1\cdot2}+\dfrac{2019}{2\cdot3}+\dfrac{2019}{3\cdot4}+...+\dfrac{2019}{2018\cdot2019}\)

\(=2019\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{2018\cdot2019}\right)\)

\(=2019\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2018}-\dfrac{1}{2019}\right)\)

\(=2019\left(1-\dfrac{1}{2019}\right)\)

\(=2019\cdot\dfrac{2018}{2019}=2018\)

Answer 2

A=2019(1/1.2+1/2.3+1/3.4+........+1/2018.2019)

A= 2019(1-1/2+1/2-1/3+1/3-......+1/2018-1/2019)

A=2019(1-1/2019)

A=2019.2018/2019

A=2018

Answer 3

= 2019. (1 - 1/2 + 1/2 - 1/3 +....+ 1/2018 -1/2019 )

= 2019 . (1 - 1/2019 )

= 2019 . 2018/2019

= 2018