Question

(X-1)/2023 +(x-2)/2022+( x-3)/2023+...+(x-2022/2

 

Answer 1

Sửa đề: \(\frac{x-1}{2023}+\frac{x-2}{2022}+\cdots+\frac{x-2022}{2}=2022\)

Ta có: \(\frac{x-1}{2023}+\frac{x-2}{2022}+\cdots+\frac{x-2022}{2}=2022\)

=>\(\left(\frac{x-1}{2023}-1\right)+\left(\frac{x-2}{2022}-1\right)+\cdots+\left(\frac{x-2022}{2}-1\right)=2022-2022=0\)

=>\(\frac{x-2024}{2023}+\frac{x-2024}{2022}+\cdots+\frac{x-2024}{2}=0\)

=>\(\left(x-2024\right)\left(\frac{1}{2023}+\frac{1}{2022}+\cdots+\frac12\right)=0\)

=>x-2024=0

=>x=2024