Question

Tìm x biết : ( 1 / 2 + 1/3 + 1/4 + ... + 1/2022) . x = 2021 / 1 + 2020 / 2+ ... + 2/2020 + 1/2021

Helpp meee!! EM CẦN GẤPPPPP

 

Answer 1

Ta có: \(\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2022}\right)\cdot x=\dfrac{2021}{1}+\dfrac{2020}{2}+...+\dfrac{1}{2021}\)

=>\(\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2022}\right)\cdot x=\left(1+\dfrac{1}{2021}\right)+\left(1+\dfrac{2}{2020}\right)+...+\left(1+\dfrac{2020}{2}\right)+1\)

=>\(x\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2022}\right)=\dfrac{2022}{2021}+\dfrac{2022}{2020}+...+\dfrac{2022}{2}+\dfrac{2022}{2022}\)

=>\(x\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2022}\right)=2022\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2022}\right)\)

=>x=2022