Ta có:

`S = 1 - 1/2 + 1/3 - 1/4 + ... + 1/2021 - 1/2022 + 1/2023`

`S = (1 + 1/3 + 1/5 + ... + 1/2023) - (1/2 + 1/4 + 1/6 + ... + 1/2022)`

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

`S = (1 + 1/2 + 1/3 + 1/4 + ... + 1/2023) - (1 + 1/2 + 1/3 + ... + 1/1011)`

`S = (1 + 1/2 + ... + 1/1011) + (1/1012 + 1/1013 + ... + 1/2023) - (1 + 1/2 + ... + 1/1011)`

`S = 1/1012 + 1/1013 + 1/1014 + ... + 1/2023`

Ta lại có:

`P = 1/1012 + 1/1013 + 1/1014 + ... + 1/2023`

Suy ra `P = S`

`=> P - S = 0`

`=> 2012 xx 2013 xx 2014 xx ... xx 2024 xx (P - S)`

`= 2012 xx 2013 xx 2014 xx ... xx 2024 xx 0`

`= 0`