Tính tổng ​\(\begin{aligned} &A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\cdots+\frac{1}{999.1000} \end{aligned}\)

* Hướng dẫn giải

Ta có:

\(\begin{aligned} &A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\cdots+\frac{1}{999.1000} \\ &A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+. .+\frac{1}{999}-\frac{1}{1000} \\ &A=1-\frac{1}{1000}=\frac{999}{1000} \end{aligned}\)