Question

Tính A : B biết:

\(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+\frac{1}{7.8}+\frac{1}{9.10}\) và \(B=\frac{1}{6.10}+\frac{1}{7.9}+\frac{1}{8.8}+\frac{1}{9.7}+\frac{1}{10.6}\)

Answer 1

A = 1/1.2 + 1/3.4 + 1/5.6 + 1/7.8 + 1/9.10

A = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10

A = ( 1 + 1/3 + 1/5 + 1/7 + 1/9) - ( 1/2 + 1/4 + 1/6 + 1/8 + 1/10)

A = ( 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10) - 2.( 1/2 + 1/4 + 1/6 + 1/8 + 1/10)

A = ( 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10) - ( 1 + 1/2 + 1/3 + 1/4 + 1/5)

A = 1/6 + 1/7 + 1/8 + 1/9 + 1/10

B = 1/6.10 + 1/7.9 + 1/8.8 + 1/9.7 + 1/10.6

16B = 16/6.10 + 16/7.9 + 16/8.8 + 16/9.7 + 16/10.6

16B = 1/6 + 1/10 + 1/7 + 1/9 + 1/8 + 1/8 + 1/9 + 1/7 + 1/10 + 1/6

16B = 2.( 1/6 + 1/7 + 1/8 + 1/9 + 1/10)

8B = 1/6 + 1/7 + 1/8 + 1/9 + 1/10

Ta có A = 8B

=> A : B = 8

Answer 2

 \(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(A=\frac{1}{2}-\frac{1}{10}\)

\(A=\frac{2}{5}\)

Answer 3

\(\text{A = 1/1.2 + 1/3.4 + 1/5.6 + 1/7.8 + 1/9.10 }\)
\(\text{= 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + 1/9 - 1/10 }\)\(\text{= ( 1 + 1/3 + 1/5 + 1/7 + 1/9) - ( 1/2 + 1/4 + 1/6 + 1/8 + 1/10)}\)

= ( 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10) - 2.( 1/2 + 1/4 + 1/6 + 1/8 + 1/10) 

= ( 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10) - ( 1 + 1/2 + 1/3 + 1/4 + 1/5) 

= 1/6 + 1/7 + 1/8 + 1/9 + 1/10

B = 1/6.10 + 1/7.9 + 1/8.8 + 1/9.7 + 1/10.6 16

   = 16/6.10 + 16/7.9 + 16/8.8 + 16/9.7 + 16/10.6 16

 = 1/6 + 1/10 + 1/7 + 1/9 + 1/8 + 1/8 + 1/9 + 1/7 + 1/10 + 1/6   

= 2.( 1/6 + 1/7 + 1/8 + 1/9 + 1/10)  

= 1/6 + 1/7 + 1/8 + 1/9 + 1/10

  Ta có A = 8B => A : B = 8