Question

Cho 𝐵 = 1.2.3. . . .2022. (1 + 1/2 + 1/3 +⋅⋅⋅ + 1/2022 ) Chứng minh rằng B chia hết cho 2023.

Answer 1

Ta có: \(B=1\cdot2\cdot3\cdot\ldots\cdot2022\cdot\left(1+\frac12+\frac13+\cdots+\frac{1}{2022}\right)\)

\(=7\cdot289\cdot1\cdot2\cdot\ldots\cdot6\cdot8\cdot\ldots\cdot288\cdot290\cdot\ldots\cdot2022\cdot\left(1+\frac12+\frac13+\cdots+\frac{1}{2022}\right)\)

\(=2023\cdot1\cdot2\cdot\ldots\cdot6\cdot8\cdot\ldots\cdot288\cdot290\cdot\ldots\cdot2022\cdot\left(1+\frac12+\frac13+\cdots+\frac{1}{2022}\right)\) ⋮2023