Question

[Le Khong Bao Minh]

Tính giá trị biểu thức

A= 2019/1x2 + 2019/2x3 + 2019/3x4 +.............+ 2019/2018x2019

Ai nhanh m tick nha

Answer 1

[Phạm Thành Đông]

\(\frac{2019}{1\times2}+\frac{2019}{2\times3}+\frac{2019}{3\times4}+...+\frac{2019}{2018\times2019}\)

\(=2019\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{2018\times2019}\right)\)

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

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

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

\(=2019\times\frac{2018}{2019}\)\(=\frac{2019\times2018}{2019}=2018\)