Question

[Hoàng Thị Bảo Yến]

2018/1.2 + 2018/2.3 + 2018/3.4 +............................ + 2018/ 2017* 2018  mình cần gấp

Answer 1

[Đức Phạm]

\(\frac{2018}{1.2}+\frac{2018}{2.3}+\frac{2018}{3.4}+...+\frac{2018}{2017.2018}\)

\(=2018\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\right)\)

\(=2018\left(1-\frac{1}{2018}\right)\)

\(=2018\cdot\frac{2017}{2018}=2017\)

Answer 2

[Thanh Tùng DZ]

\(\frac{2018}{1.2}+\frac{2018}{2.3}+\frac{2018}{3.4}+...+\frac{2018}{2017.2018}\)

\(2018.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\right)\)

\(2018.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\right)\)

\(2018.\left(1-\frac{1}{2018}\right)\)

\(2018-1=2017\)