Ta có:\(\dfrac{20}{2\times7}+\dfrac{20}{7\times12}+\dfrac{20}{12\times17}+\dfrac{20}{17\times22}+\dfrac{20}{22\times27}+\dfrac{20}{27\times32}\)
\(=4\times\left(\dfrac{5}{2\times7}+\dfrac{5}{7\times12}+\dfrac{5}{12\times17}+\dfrac{5}{17\times22}+\dfrac{5}{22\times27}+\dfrac{5}{27\times32}\right)\)
\(=4\times\left(\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{22}+\dfrac{1}{22}-\dfrac{1}{27}+\dfrac{1}{27}-\dfrac{1}{32}\right)\)
\(=4\times\left(\dfrac{1}{2}-\dfrac{1}{32}\right)=4\times\dfrac{15}{32}=\dfrac{30}{16}\)
\(\dfrac{20}{2\cdot7}+\dfrac{20}{7\cdot12}+\dfrac{20}{12\cdot17}+\dfrac{20}{17\cdot22}+\dfrac{20}{22\cdot27}+\dfrac{20}{27\cdot32}\) ( * là nhân nha )
20 x ( \(\dfrac{1}{2\cdot7}+\dfrac{1}{7\cdot12}+\dfrac{1}{12\cdot17}+\dfrac{1}{17\cdot22}+\dfrac{1}{22\cdot27}+\dfrac{1}{27\cdot32}\) )
20 x ( \(\dfrac{1}{2}+\dfrac{1}{7}-\dfrac{1}{7}+\dfrac{1}{12}-\dfrac{1}{12}+\dfrac{1}{17}-\dfrac{1}{17}+\dfrac{1}{22}-\dfrac{1}{22}+\dfrac{1}{27}-\dfrac{1}{27}+\dfrac{1}{32}\) )
20 x ( \(\dfrac{1}{2}-\dfrac{1}{32}\) )
20 x \(\dfrac{15}{32}\) = \(\dfrac{300}{32}=\dfrac{75}{8}\)
Ta có: \(\dfrac{20}{2\cdot7}+\dfrac{20}{7\cdot12}+...+\dfrac{20}{27\cdot32}\)
\(=4\left(\dfrac{5}{2\cdot7}+\dfrac{5}{7\cdot12}+\dfrac{5}{12\cdot17}+...+\dfrac{5}{27\cdot32}\right)\)
\(=4\left(\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{12}+...+\dfrac{1}{27}-\dfrac{1}{32}\right)\)
\(=4\left(\dfrac{1}{2}-\dfrac{1}{32}\right)\)
\(=4\cdot\dfrac{15}{32}=\dfrac{15}{8}\)
