`A = ( 1/2^2 - 1 ) . ( 1/3^2 - 1 ) . ( 1/4^2 - 1 ) .... ( 1/100^2 - 1 )`
`A = ( 1/4 - 1 ) . ( 1/9 - 1 ) . ( 1/16 - 1 ) .... ( 1/10000 - 1 )`
`A = ( - 3 )/4 . ( - 8 )/9 . ( - 15 )/16 .... ( - 9999 )/10000`
`A = ( ( - 3 ) . ( - 8 ) . ( - 15 ) .... ( - 9999 ) )/( 4 . 9 . 16 .... 10000 )`
`A = ( ( - 1 ) . 3 . ( - 2 ) . 4 . ( - 3 ) . 5 .... ( - 99 ) . 101 )/( 2 . 2 . 3 . 3 . 4 . 4 .... 100 . 100 )`
`A = ( [ ( - 1 ) . ( - 2 ) . ( - 3 ) .... ( - 99 ) ] . ( 3 . 4 . 5 .... 101 ) )/( ( 2 . 3 . 4 ... 100 ) . ( 2 . 3 . 4 .... 100 ) )`
`A = ( ( - 1 ) . 101 )/( 100 . 2 )`
`A = ( - 101 )/200 < ( - 100 )/200 = ( - 1 )/2`
`⇒ A < ( - 1 )/2`
Vậy `, A < ( - 1 )/2 .`