Tính tổng: 2/1*3 + 2/3*5 + 2/5*7 +...+2/99*101 Ta có 2/1*3 + 2/3*5+...+ 2/99*101

* Hướng dẫn giải

$$\begin{gathered} Ta có: \frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\mathrm{...}+\frac{2}{99.101} \\ =\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+\mathrm{...}+\frac{101-99}{99.101} \\ =\frac{3}{1.3}-\frac{1}{1.3}+\frac{5}{3.5}-\frac{3}{3.5}+\frac{7}{5.7}-\frac{5}{5.7}+\mathrm{...}+\frac{101}{99.101}-\frac{99}{99.101} \\ =1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\mathrm{...}+\frac{1}{99}-\frac{1}{101} \\ =1-\frac{1}{101} \\ Vậy: \frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\mathrm{...}+\frac{2}{99.101}=\frac{100}{101} \end{gathered}$$