đăt A= đề bài ta có A=1-1/2+1/2-1/3+1/3-1/4+...+1/2017-1/2018
A=1-1/2018=2017/2018
Ta có :
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)
\(=\)\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(=\)\(1-\frac{1}{2018}\)
\(=\)\(\frac{2017}{2018}\)
Chúc bạn học tốt ~
1/1×2 + 1/2×3 + 1/3×4 +......+ 1/2017×2018
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +.......+ 1/2017 - 1/2018
= 1 - 1/2018
= 2017/2018
