Question

Tính giá trị biểu thức:         

M = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ... + 1/10.11.12

Answer 1

\(M=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{10.11}-\frac{1}{11.12}\)

\(=\frac{1}{2}-\frac{1}{11.12}\)

\(=\frac{65}{132}\)

Answer 2

Ta có nhận xét: 1/1.2 - 1/2.3 = 3-1/1.2.3 = 2/1.2.3          

                       1/2.3 - 1/3.4 = 4-2/2.3.4 = 2/2.3.4      

Suy ra:             1/1.2.3 = 1/2(1/1.2 - 1/2.3)    

                         1/2.3.4 = 1/2(1/2.3 -1/3.4)  

Do đó:              M = 1/2(1/1.2-1/2.3 + 1/2.3 -1/3.4 + ... + 1/10.11 -1/11.12)

                           = 1/2(1/1.2 - 1/11.12) = 1/2(1/2-11/12 )      

                           = 1/2.65/132 = 65/264

Phức tạp lắm

Answer 3

Bạn ơi nhưng 1/(1.2.3) không bằng 1/(1.2) -1/(2.3)?

Answer 4

bai nay de lam de trua minh hoc ve minh lam cho nha

Answer 5

B = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + .... + 1/10.11.12

suy ra 2B = 2/1.2.3 + 2/2.3.4 + 2/3.4.5 + .... +1/10.11.12

2B = 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + .... + 1/10.11 + 1/11.12

2B = 1/1.2 - 1/11.12

     = 1/2 - 1/11.12

     = 1/2 - 1/132 

     = 65 / 132

suy ra 2B = 65/132

suy ra B = 65/132 : 2 

          B = 65/264