Tìm x, biết: x+`x/(1+2)`+`x/(1+2+3)`+…+`x/(1+2+…+4041)`=4041

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1. Đáp án:

   `x=2021`

   Giải thích các bước giải:

   `x+x/(1+2)+x/(1+2+3)+…+x/(1+2+3+…+4041)=4041`

   `=>x*(1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+…+4041))=4041`
   `=>`$x\cdot\left(1+\dfrac{1}{3}+\dfrac{1}{6}\ \!\! +\ \!\!.\!.\!.+\ \dfrac{1}{\dfrac{(4041+1).4041}{2}}\right)=4041$
   `=>`$x\cdot\left(1+\dfrac{1}{3}+\dfrac{1}{6}\ \!\!+\ \!\!.\!.\!.+\ \dfrac{1}{\dfrac{4042.4041}{2}}\right)=4041$

   `=>2x*(1/2+1/6+1/12+…+1/4041.4042)=4041`

   `=>2x*(1/1.2+1/2.3+1/3.4+…+1/4041.4042)=4041`

   `=>2x*(1-1/2+1/2-1/3+1/3-1/4+1/4+…+1/4041-1/4042)=4041`

   `=>2x*(1-1/4042)=4041`

   `=>2x*4041/4042=4041`

   `=>2x=4041:4041/4042`

   `=>2x=4042`

   `=>x=4042:2`

   `=>x=2021`

   Vậy `x=2021`.

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2. Đáp án + Giải thích các bước giải:

   `x+x/(1+2)+x/(1+2+3)+…+x/(1+2+…+4041)=4041`
   `=>x(1+1/(1+2)+1/(1+2+3)+…+1/(1+2+…+4041))=4041`
   `=>x[1+1/((2(2+1))/2)+1/((3(3+1))/2)+…+1/((4041(4041+1))/2)]=4041`
   `=>2x[1/1.2+1/(2.3)+1/(3.4)+…+1/(4041.4042)]=4041`
   `=>2x[1/1-1/2+1/2-1/3+1/3-1/4+…+1/4041-1/4042]=4041`
   `=>2x[1/1-1/4042]=4041`
   `=>2x[4042/4042-1/4042]=4041`
   `=>2x. 4041/4042=4041`
   `=>2x. 4041/4042=4041`
   `=>2x=4041:4041/4042`
   `=>2x=4041. 4042/4041`
   `=>2x=4042`
   `=>x=4042:2`

   `=>x=2021`

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