Ta thấy
\(\dfrac{1}{4\times6}=\dfrac{1}{4\times3\times1\times2}=\dfrac{1}{4\times3}\times\dfrac{1}{1\times2}\)
\(\dfrac{1}{8\times9}=\dfrac{1}{4\times2\times3\times3}=\dfrac{1}{4\times3}\times\dfrac{1}{2\times3}\)
.....................
\(\dfrac{1}{2680\times2013}=\dfrac{1}{4\times670\times3\times671}=\dfrac{1}{4\times3}\times\dfrac{1}{670\times671}\)
Vì \(\dfrac{1}{4\times6}+\dfrac{1}{8\times9}+...+\dfrac{1}{2680\times2013}\)
=> \(\dfrac{1}{4\times3}\times\dfrac{1}{1\times2}+\dfrac{1}{4\times3}\times\dfrac{1}{2\times3}+.....+\dfrac{1}{4\times3}\times\dfrac{1}{670\times671}\)
=> \(\dfrac{1}{4\times3}\times\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{670\times671}\right)\)
=> \(\dfrac{1}{12}\times\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{670}-\dfrac{1}{671}\right)\)
=> \(\dfrac{1}{12}\times\left(1-\dfrac{1}{671}\right)\)
=> \(\dfrac{1}{12}\times\dfrac{670}{671}=\dfrac{335}{4026}\)
bn xem lại đề nhé
\(\dfrac{1}{2680\times20}\) thì ko ra công thức đc
