Tính nhanh: A= 1+ 1/8+1/24+1/48+1/80+1/120 Ta có 1+5/12 = 17/12

* Hướng dẫn giải

Lời giải

$$\begin{gathered} Ta có: A=1+\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120} \\ =1+\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12} \\ =1+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}\right)+\frac{1}{2}\left(\frac{1}{4}-\frac{1}{6}\right)+\frac{1}{2}\left(\frac{1}{6}-\frac{1}{8}\right)+\frac{1}{2}\left(\frac{1}{8}-\frac{1}{10}\right)+\frac{1}{2}\left(\frac{1}{10}-\frac{1}{12}\right) \\ =1+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}\right) \\ =1+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{12}\right) \\ =1+\frac{1}{2}.\frac{5}{12} \\ =1+\frac{5}{12}=\frac{17}{12} \\ Vậy A=1+\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+\frac{1}{120}=\frac{17}{12} \end{gathered}$$