Câu trả lời:
A=\(\frac{1}{1.2}+....+\frac{1}{2013.2014}+\frac{1}{2015.2016}\)=\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2015}-\frac{1}{2016}\)
=\(\left(1+\frac{1}{3}+.....+\frac{1}{2015}\right)-\left(\frac{1}{2}+\frac{1}{4}+....+\frac{1}{2016}\right)\)
=\(\left(1+\frac{1}{2}+.....+\frac{1}{2016}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+....+\frac{1}{2016}\right)\)