Question

2023-1/2*(1+2)-1/3*(1+2+3)-1/4*(1+2+3+4)-...-1/2022*(1+2+3+4+...+2022)

Answer 1

Ta có: \(2023-\frac12\left(1+2\right)-\frac13\left(1+2+3\right)-\cdots-\frac{1}{2022}\left(1+2+\cdots+2022\right)\)

\(=2023-\frac12\cdot\frac{2\cdot3}{2}-\frac13\cdot\frac{3\cdot4}{2}-\cdots-\frac{1}{2022}\cdot\frac{2022\cdot2023}{2}\)

\(=2023-\frac32-\frac42-\cdots-\frac{2023}{2}=2023-\frac12\left(3+4+\cdots+2023\right)\)

\(=2023-\frac12\frac{\left(2023-3+1\right)\left(2023+3\right)}{2}=2023-\frac12\cdot\frac{2021\cdot2026}{2}=2023-\frac12\cdot2021\cdot1013\)

=-1021613,5