Tính tổng sau B = 1/1.2.3.4 + 1/2.3.4.5 + 1/3.4.5.6 +...+ 1/27.28.29.30

* Hướng dẫn giải

$$\begin{gathered} B=\frac{1}{\mathrm{1.2.3.4}}+\frac{1}{\mathrm{2.3.4.5}}+\frac{1}{\mathrm{3.4.5.6}}+\mathrm{...}+\frac{1}{\mathrm{27.28.29.30}} \\ \begin{array}{l}=\frac{1}{3}\left(\frac{1}{\mathrm{1.2.3}}-\frac{1}{\mathrm{2.3.4}}+\frac{1}{\mathrm{2.3.4}}-\frac{1}{\mathrm{3.4.5}}+\mathrm{...}+\frac{1}{\mathrm{27.28.29}}-\frac{1}{\mathrm{28.29.30}}\right)\\ =\frac{1}{3}\left(\frac{1}{\mathrm{1.2.3}}-\frac{1}{\mathrm{28.29.30}}\right)=\frac{1353}{8120}\end{array} \end{gathered}$$