Bn tham khảo nhé :
2 / 2 . 3 + 2 /3 . 4 + 2 / 4 .5 + ... + 2 / 2017 . 2018
= 2 . ( 1/2 . 3 + 1/3 . 4 + 1/4 . 5 + ... + 1/ 2017 . 2018
= 2 . ( 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/2017 - 1/2018 )
= 2 . ( 1/2 - 1/2018)
= 2 . 1008/2018
= 2016/2018
= 1008/1009
\(2\times(\frac{1}{2\times3}\times\frac{1}{3\times4}\times...\times\frac{1}{2017\times2018}))\)
\(2\times(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018})\)
\(2\times(\frac{1}{2}-\frac{1}{2018})\)
\(2\times\frac{504}{1009}=\frac{1008}{1009}\)
\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+.......+\frac{2}{2017.2018}\)
\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.......+\frac{1}{2017.2018}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-.........-\frac{1}{2017}-\frac{1}{2018}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{2018}\right)\)
\(=2\left(\frac{1009}{2018}-\frac{1}{2018}\right)\)
\(=2.\frac{1008}{2018}\)
\(=\frac{1008}{1009}\)
