`A = 2/(1.2.3) + 2/(2.3.4) + 2/(3.4.5) + ... + 2/(2013.2014.2015)`
`A = 1/(1.2) - 1/(2.3) + 1/(2.3) - 1/(3.4) + 1/(3.4) - 1/(4.5) + ... + 1/(2013.2014) - 1/(2014.2015)`
`A = 1/(1.2) - 1/(2014.2015)`
`A = 1/2 - 1/(2014.2015)`
Mà `1/2 - 1/(2014.2015) < 1/2`
`<=> A < 1/2`
`<=> A < B`
Vậy `A < B`