\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+...+\dfrac{4}{2015.2017}\)
= 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