`A=(1/2^2-1).(1/3^2-1).(1/4^2-1)...(1/40^2-1)`
`= (-3)/4 . (-8)/9 . (-15)/16 ... (-1599)/1600`
`= -(3/4 . 8/9 . 15/16 ... 1599/1600)`
`=-((1.3)/(2.2).(2.4)/(3.3).(3.5)/(4.4)...(39.41)/(40.40))`
`=-((1.2.3...39).(3.4.5...41))/((2.3.4...40).(2.3.4...40))`
`=-41/(40.2)=(-41)/80<(-40)/80=(-1)/2`
$\text{Vậy}$ `A < (-1)/2`