mình ko chép lại đề nhé, sửa 2014 + 2016 thành 2014.2016
\(A=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2014}-\dfrac{1}{2016}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{2016}\right)=2\left(\dfrac{2016-2}{6032}\right)=\dfrac{2.2018}{6032}=\dfrac{4036}{6032}=\dfrac{1009}{1508}\)
\(A=\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+...+\dfrac{4}{2014.2016}\)
\(=2\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{2014.2016}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2014}-\dfrac{1}{2016}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{2016}\right)\)
\(=2.\dfrac{1007}{2016}=\dfrac{1007}{1008}\)
Giải:
Sửa đề 4/2014+2016 ➜ 4/2014.2016
A=4/2.4+4/4.6+4/6.8+...+4/2014.2016
A=2.(2/2.4+2/4.6+2/6.8+...+2/2014.2016)
A=2.(2/2-2/4+2/4-2/6+2/6-2/8+...+2/2014-2/2016)
A=2.(2/2-2/2016)
A=2.1007/1008
A=1007/504
Chúc bạn học tốt!
