Answer
`A = (1/4 - 1) . (1/9 - 1) . (1/16 - 1) ... (1/100 - 1)`
`A = (1/4 - 4/4) . (1/9 - 9/9) . (1/16 - 16/16) ... (1/100 - 100/100)`
`A = {-3}/4 . {-8}/9 . {-15}/16 ... {-99}/100`
`A = {1 . (-3)}/{2 . 2} . {2 . (-4)}/{3 . 3} . {3 . (-5)}/{4 . 4} ... {9 . (-11)}/{10 . 10}`
`A = - ({1 . 2 . 3 ... 9}/{2 . 3 . 4 ... 10} . {3 . 4 . 5 ... 11}/{2 . 3 . 4 ... 10})`
`A = - (1/10 . 11/2)`
`A = {-11}/20`
Ta có:
`20 < 21`
`=> {-11}/20 < {-11}/21`
`=> A < {-11}/21`
Vậy `A < {-11}/21`
