Tính: A = 2/1.3 + 2/3.5 + 2/5.7 + ...+ 2/99.101

* Hướng dẫn giải

$\begin{array}{l}A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\mathrm{...}+\frac{2}{99.101}\\ =1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\mathrm{...}+\frac{1}{99}-\frac{1}{101}\\ =1-\frac{1}{101}=\frac{100}{101}\end{array}$