\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+...........+\dfrac{4}{2015.2017}\)
\(=2\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+............+\dfrac{2}{2015.2017}\right)\)
\(=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+.........+\dfrac{1}{2015}-\dfrac{1}{2017}\right)\)
\(=2\left(1-\dfrac{1}{2017}\right)\)
\(=2.\dfrac{2016}{2017}=\dfrac{4032}{2017}\)
\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+...+\dfrac{4}{2015.2017}\)
= 2.(\(\dfrac{2}{1.3}+\dfrac{1}{3.5}+...+\dfrac{2}{2015.2017}\))
= 2.(1 - \(\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2015}-\dfrac{1}{2017}\))
= 2.(1 - \(\dfrac{1}{2017}\))
= 2.\(\dfrac{2016}{2017}\)
= \(\dfrac{4032}{2017}\)
@Nguyễn Thị Ngọc Anh
