Giúp mk vs nhanh nhé mk cần gấp lắm ạ cám ơn nhìu

`A = ( 1 - 1/( 1 + 2 ) ) . ( 1 - 1/( 1 + 2 + 3 ) ) .... ( 1 - 1/( 1 + 2 + 3 + .... + 2022 ) )`

`A = ( 1 - 1/( ( ( 2 + 1 ) . 2 )/2 ) ) . ( 1 - 1/( ( ( 3 + 1 ) . 3 )/2 ) ) .... ( 1 -1/( ( ( 2022 + 1 ) . 2022 )/2 ) )`

`A = ( 1 - 2/( 2 . ( 1 + 2 ) ) ) . ( 1 - 2/( 3 . ( 3 + 1 ) ) ) .... ( 1 - 2/( 2022 . ( 2022 + 1 ) ) )`

`A = ( 1 - 2/( 2 . 3 ) ) . ( 1 - 2/( 3 . 4 ) ) .... ( 1 - 2/( 2022 . 2023 ) )`

`A = ( 2 . 3 - 2 )/( 2 . 3 ) . ( 3 . 4 - 2 )/( 3 . 4 ) .... ( 2022 . 2023 - 2 )/( 2022 . 2023 )`

Xét `n . ( n + 1 ) - 2 = n^2 + n - 2 = n^2 - n + 2n - 2 = n ( n - 1 ) + 2 ( n - 1 ) = ( n - 1 ) ( n + 2 )`

`=> A = ( ( 2 - 1) . ( 2 + 2 ) )/( 2 .  3 ) . ( ( 3 - 1 ) . (  3+ 2 ) )/( 3 . 4 ) ..... ( ( 2022 - 1 ) . ( 2022 + 2 ) )/( 2022 . 2023 )`

`A = ( 1 . 4 )/( 2 . 3 ) . ( 2 . 5 )/( 3 . 4 ) .... ( 2021 . 2024 )/( 2022 . 2023 )`

`A = ( ( 1 . 4 ) . ( 2 . 5 ) .... ( 2021 . 2024 ) )/( ( 2 . 3 ) . ( 3 . 4 ) .... ( 2022 . 2023 ) )`

`A = ( ( 1 . 2 .... 2021 ) . ( 4 . 5 .... 2024 ) )/( ( 2 . 3 .... 2022 ) . ( 3 . 4 .... 2023 ) )`

`A = ( 1 . 2024 )/( 2022 . 3 )`

`A = 2024/6066 = 1012/3033`

Vậy `, A = 1012/3033 .`