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