Question

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2018.2019}\)

 

Answer 1

=1 - 1/3 +1/3 -1/5 +1/5 -1/7 +.........+1/2018 - 1/2019

=1 - 1/2019

=2018/2019

K MK NHA. CHÚC BẠN HỌC GIỎI

Answer 2

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{2017.2019}\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{2019}\right)\)

\(=\frac{1}{2}.\frac{2018}{2019}\)

\(=\frac{1009}{2019}\)

Answer 3

\(=\frac{2}{2}\cdot\left(\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+.....+\frac{1}{2018\cdot2019}\right)\)

Answer 4

xin lỗi tôi viết nhầm đề chữa lại là \(\frac{1}{2017.2018}\)