`A = 1/2 + 1/12 + 1/30 + ... + 1/(2015. 2016)`
`= 1/(1. 2) + 1/(3. 4) + 1/(5. 6) + ... + 1/(2015. 2016)`
`= 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... + 1/2015 - 1/2016`
`= (1 + 1/3 + 1/5 + ... + 1/2015) - (1/2 + 1/4 + 1/6 + ... + 1/2016)`
`= (1 + 1/3 + 1/5 + ... + 1/2015) + (1/2 + 1/4 + 1/6 + ... + 1/2016) - 2(1/2 + 1/4 + 1/6 + ... + 1/2016)`
`= (1 + 1/2 + 1/3 + 1/4 + ... + 1/2015 + 1/2016) - (1 + 1/2 + 1/3 + ... + 1/1008)`
`= (1 + 1/2 + 1/3 + ... + 1/1008) + (1/1009 + 1/1010 + ... + 1/2015 + 1/2016) - (1 + 1/2 + 1/3 + ... + 1/2008)`
`= 1/1009 + 1/1010 + ... + 1/2015 + 1/2016`
`B = 2016/1009 + 2016/1010 + ... + 2016/2015 + 1`
`= 2016(1/1009 + 1/1010 + ... + 1/2015 + 1/2016)`
`= 2016. A`
`=> B/A - 1 = (2016. A)/A - 1 = 2016 - 1 = 2015 vdots 5`
Vậy `B/A - 1 vdots 5`