1/2+1/6+1/12+1/20+….+1/x(x+1)=2021/2022 nhanh lên ạ

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1. Đáp án + Giải thích các bước giải:

   `1/2+1/6+1/12+1/20+…+1/(x(x+1))=2021/2022`

   `=>1/1.2+1/2.3+1/3.4+1/4.5+…+1/(x(x+1))=2021/2022`

   `=>1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…+1/x-1/(x+1)=2021/2022`

   `=>1/1-1/(x+1)=2021/2022`

   `=>1/(x+1)=1/1-2021/2022`

   `=>1/(x+1)=2022/2022-2021/2022`

   `=>1/(x+1)=1/2022`

   `=>x+1=2022`

   `=>x=2022-1`

   `=>x=2021`

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2. Đáp án:

    x=2021

   Giải thích các bước giải:

    1/2+1/6+…+1/x(x+1)=2021/2022

   ⇒1/1×2+1/2×3+…+1/x(x+1)=2021/2022

   ⇒1-1/2+1/2-1/3+…+1/x-1/x+1=2021/2022

   ⇒1-1/x+1=2021/2022

   ⇒1/x+1=1-2021/2022

   ⇒1/x+1=1/2022

   ⇒x+1=2022

   ⇒x=2022-1

   ⇒x=2021

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