Tính tổng sau A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 +...+ 1/98.99.100

* Hướng dẫn giải

$$\begin{gathered} A=\frac{1}{\mathrm{1.2.3}}+\frac{1}{\mathrm{2.3.4}}+\frac{1}{\mathrm{3.4.5}}+\mathrm{...}+\frac{1}{\mathrm{98.99.100}} \\ \begin{array}{l}=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\mathrm{...}+\frac{1}{98.99}-\frac{1}{99.100}\\ =\frac{1}{1.2}-\frac{1}{99.100}=\frac{4949}{19800}\end{array} \end{gathered}$$