Đáp án+Giải thích các bước giải:
`P=(1/2^2 -1)(1/3^2-1)(1/4^2-1).......(1/2021^2-1)`
`=3/2^2 * 8/(3^2) * 15/4^2 *.......* (2020*2022)/2021^2`
`=(1*3)/(2^2)*(2*4)/(3^2)*(3*5)/(4^2)*.....*(2020*2022)/(2021^2)`
`=[(1*3)*(2*4)*(3*5)*........*(2020*2022)]/(2^2 * 3^2 *4^2 * .....*2021^2)`
`=[(1*2*3*.....*2020)(3*4*5*.....*2022)]/[(2*3*4*......*2021)(2*3*4*.....*2021)]`
`=(1*2022)/(2021*2)`
`=1011/2021 `
Vì `1/2=1011/2022 < 1011/2021`
`-> P > 1/2`
Vậy `P > 1/2`
