`N= 4/2.4 + 4/4.6 + 4/6.8 +...+ 4/2014.2016`
`N= 2( 2/2.4 + 2/4.6 + 2/6.8 +...+ 2/2014.2016)`
`N=2 ( ( 4-2)/(2.4) + (6-4)/4.6 + .... + (2016-2014)/2014.2016)`
`N= 2 ( 4/2.4 - 2/2.4 + 6/4.6 - 4/6.4 +...+ 2016/2014.2016 - 2014/2014.2016)`
`N= 2( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 -...+ 1/2014 - 1/2016)`
`N= 2. ( 1/2- 1/2016)`
`N= 2. 1007/2016`
`N= 1007/1008`
Vậy `N= 1007/1008`