Question

( 1/2 + 1/3 + ... + 1/2022 + 1/2023 ) .x = 2022/1 + 2021/2 + ... + 2/2021 + 1/2022

Answer 1

( 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

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Answer 2

Lời giải:

$\frac{2022}{1}+\frac{2021}{2}+\frac{2020}{3}+....+\frac{2}{2021}+\frac{1}{2022}$

$=2022+\frac{2021}{2}+\frac{2020}{3}+....+\frac{2}{2021}+\frac{1}{2022}$

$=1+(1+\frac{2021}{2})+(1+\frac{2020}{3})+....+(1+\frac{2}{2021})+(1+\frac{1}{2022})$

$=\frac{2023}{2}+\frac{2023}{3}+...+\frac{2023}{2021}+\frac{2023}{2022}+1$

$=\frac{2023}{2}+\frac{2023}{3}+...+\frac{2023}{2021}+\frac{2023}{2022}+\frac{2023}{2023}$

$=2023\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2022}+\frac{1}{2023}\right)$

$\Rightarrow x=2023$