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

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})