( 1/2 + 1/3 + ... + 1/2022 + 1/2023 ).x =2023/2023+2023/2022+2023/2021+2023/2020+...+2023/2
( 1/2 + 1/3 + ... + 1/2022 + 1/2023 ).x=2023.(1/2 + 1/3 + ... + 1/2022 + 1/2023)
x=2023
chúc bạn học tốt nha!
Lời giải:
$\frac{2022}{1}+\frac{2021}{2}+\frac{2020}{3}+....+\frac{2}{2021}+\frac{1}{2022}$
$=2022+\frac{2021}{2}+\frac{2020}{3}+....+\frac{2}{2021}+\frac{1}{2022}$
$=1+(1+\frac{2021}{2})+(1+\frac{2020}{3})+....+(1+\frac{2}{2021})+(1+\frac{1}{2022})$
$=\frac{2023}{2}+\frac{2023}{3}+...+\frac{2023}{2021}+\frac{2023}{2022}+1$
$=\frac{2023}{2}+\frac{2023}{3}+...+\frac{2023}{2021}+\frac{2023}{2022}+\frac{2023}{2023}$
$=2023\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2022}+\frac{1}{2023}\right)$
$\Rightarrow x=2023$
