1008 các bạn sửa lại giúp mink là 2008
\(\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+............+\dfrac{4}{2008.2010}\)
\(=2\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+......+\dfrac{2}{2008.2010}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+....+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{2010}\right)\)
\(=2.\dfrac{502}{1005}=\dfrac{1004}{1005}\)
Đặt \(A=\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+...+\dfrac{4}{2008.2010}\)
\(A=4.\dfrac{1}{2}.\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{2008.2010}\right)\)
\(A=2.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)
\(A=2.\left(\dfrac{1}{2}-\dfrac{1}{2010}\right)\)
\(A=1-\dfrac{2}{2010}\)
\(A=1-\dfrac{1}{1005}\)
