Tìm x sao cho (1/2 + 1/4 + 1/8 + 1/16) : x = 1/2 + 1/6 + 1/12 +1/20 + … + 1/132

0 bình luận về “Tìm x sao cho (1/2 + 1/4 + 1/8 + 1/16) : x = 1/2 + 1/6 + 1/12 +1/20 + … + 1/132”

1. Đáp án:

    `x=45/44`

   Giải thích các bước giải:

   `(1/2 + 1/4 + 1/8 + 1/16) : x = 1/2 + 1/6 + 1/12 +1/20 + … + 1/132`

   `=>` `(1/2 + 1/4 + 1/8 + 1/16) : x = 1/1.2 + 1/2.3 + 1/3.4 +1/4.5 + … + 1/11.12`

   `=>` `(1/2 + 1/4 + 1/8 + 1/16) : x = 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…+1/11-1/12`

   `=>` `(1/2 + 1/4 + 1/8 + 1/16) : x = 1-(1/2-1/2+1/3-1/3+1/4-1/4+1/5-…-1/11+1/12)`

   `=>` `(1/2 + 1/4 + 1/8 + 1/16) : x = 1-1/12`

   `=>` `(1/2 + 1/4 + 1/8 + 1/16) : x = 11/12`

   `=>` `x=(1/2+1/4+1/8+1/16) : 11/12`

   `=>` `x=11/12×(8/16+4/16+2/16+1/16) : 11/12`

   `=>` `x=15/16 : 11/12`

   `=>` `x=45/44`

   Bình luận

2. Xét: 

   A = 1/2 + 1/4 + 1/8 + 1/16

   2A = 1 + 1/2 + 1/4 + 1/8

   2A – A = 1 – 1/16

   => A = 15/16

   Xét: 

   B=1/2 + 1/6 + 1/12 +…+ 1/132
   B=1/1.2 +1/2.3 +1/3.4 +… +1/11.12
   B=1 – 1/1 +1/2 -1/3 +1/3 -1/4 +… +1/11 -1/12
   B=1 – 1/12
   =>B=11/12
   Thay vào ta có
   15/16 : x =11/12
   =>x =15/16 : 11/12
   =>x = 45/44

    

   Bình luận