tìm x biết 1/20+1/44+1/77+…12/x×(x+3)=101/770

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1. Đáp án:

   `x=305`

   Giải thích các bước giải:

   `1/20+1/44+1/77+…+2/(x(x+3))=101/770`

   `=>1/20+1/44+1/77+…+1/(x(x+3)÷2)=101/770`

   `=>1/40+1/88+1/154+…+1/(x(x+3))=101/1540`

   `=>1/5.8+1/8.11+1/11.14+…+1/(x(x+3))=101/1540`

   `=>1/3(3/5.8+3/8.11+3/11.14+…+3/(x(x+3)))=101/1540`

   `=>1/3(1/5-1/8+1/8-1/11+1/11-1/14+…+1/x-1/(x+3))=101/1540`

   `=>1/3(1/5-1/(x+3))=101/1540`

   `=>1/5-1/(x+3)=101/1540÷1/3`

   `=>1/5-1/(x+3)=303/1540`

   `=>1/(x+3)=1/5-303/1540`

   `=>1/(x+3)=1/308`

   `=>x+3=308`

   `=>x=308-3`

   `=>x=305`

   Vậy `x=305`.

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2. 1/20+1/44+1/77+…+2/x(x+3)=101/770
   =>3/2.[1/20+1/44+1/77+…+2/x(x+3)]=101/770.3/2
   =>3/40+3/88+3/154+…+3/x(x+3)=303/1540
   =>3/5.8+3/8.11+3/11.14+…+3/x(x+3)=303/1540
   =>1/5-1/8+1/8-1/11+1/11-1/14+…+1/x-1/x+3=303/1540
   =>1/5-1/x+3=303/1540
   =>1/x+3=1/5-303/1540
   =>1/x+3=308/1540-303/1540
   =>1/x+3=5/1540
   =>1/x+3=1/308
   =>x+3=308
   =>x=308-3
   =>x=305

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