x-20/11×13-20/13×15-20/15×17-…-20/53×55=3/11 1/3+1/6+1/10+2/x(x+1)=2003/2004

0 bình luận về “x-20/11×13-20/13×15-20/15×17-…-20/53×55=3/11 1/3+1/6+1/10+2/x(x+1)=2003/2004”

1. Đáp án + Giải thích các bước giải:

   `x – 20/(11*13) – 20/(13*15) – 20/(15*17)-…-20/(53*55)=3/11` $\\$ `=> x – (20/(11*13) + 20/(13*15)+20/(15*17)+…+20/(53*55))=3/11` $\\$ `=>x – [10(2/(11*13)+2/(13*15) + 2/(15*17) + … + 2/(53*55))]=3/11` $\\$ `=>x – [10*(1/11 – 1/13 + 1/13 – 1/15 + … + 1/53 – 1/55)]=3/11` $\\$ `=> x – [10*(1/11 – 1/55)] = 3/11` $\\$ `=> x – (10*4/55) = 3/11` $\\$ `=> x – 8/11 = 3/11 => x = 3/11 + 8/11 = 11/11 = 1`

   Vậy `x = 1`

   `1/3 + 1/6 + 1/10 +… + 2/[x(x + 1)] = 2003/2004` $\\$ `=> 2/6+2/12+2/20+…+2/[x(x+1)] = 2003/2004` $\\$ `=> 2/(2*3) + 2/(3*4) + 2/(4*5) + … + 2/[x(x+1)]=2003/2004` $\\$ `=> 2(1/(2*3) + 1/(3*4) + 1/(4*5) + … + 1/[x(x + 1)]) = 2003/2004` $\\$ `=> 2(1/2 – 1/3 + … + 1/x – 1/(x + 1)) = 2003/2004` $\\$ `=> 2(1/2 – 1/(x + 1)) = 2003/2004` $\\$ `=> 1/2 – 1/(x + 1) = 2003/4008` $\\$ `=> 1/(x + 1) = 1/2 – 2003/4008 = 1/4008` $\\$ `=> x + 1 = 4008 => x = 4007`

   Vậy `x = 4007` 

   Bình luận