`\color{#1c1c1c}{\text{I}}^(\color{#363636}{\text{t}}^(\color{#4f4f4f}{\text{s}}^(\color{#696969}{\text{m}}^(\color{#828282}{\text{e}}^(\color{#9c9c9c}{\text{F}}^(\color{#b5b5b5}{\text{r}}^(\color{#cfcfcf}{\text{e}}^\color{#eee9e9}{\text{d}})))))))`

Ta có:

`P = 1 . 2 . 3 . 4 . ... . 2024 . (1 + 1/2 + 1/3 + ... + 1/2024)`

`P = 1 . 2 . 3 . 4 . ... . 2014 . [(1 + 1/2024) + (1/2 + 1/2023) + ... + (1/1012 + 1/1013)]`

`P = 1 . 2 . 3 . 4 . ... . 2014 . [2025/(1 . 2024) + 2025/(2 . 2023) + ... + 2025/(1012 . 1013)]`

`P = 1 . 2 . 3 . 4 . ... . 2024 . 2025 . [1/1 . 2014 + 1/(2 . 2023) + ... + 1/(1012 . 1013)]`

     Vì `P` có một thừa số là `2025 \vdots 2025` nên `P \vdots 2025`

            Vậy: `P \vdots 2025`