`A = 2000/2001 + 2001/2002 + ... + 2015/2016`
$\text{Ta có : }$`2000/2001 < 1`
`2001/2002 < 1`
`....................`
`2015/2016 < 1`
`=> 2000/2001 + 2001/2002 + ... + 2015/2016 < 1 + 1 + 1 + ... + 1`
`=> 2000/2001 + 2001/2002 + ... + 2015/2016 < 15`
`=> A < 15`