Đáp án:
`301/2`
Giải thích các bước giải:
`A=1/(1.2)+1/(3.4)+....+1/(199.200)`
`=1/1-1/2+1/3-1/4+...+1/199-1/200`
`=(1+1/3+...+1/199)-(1/2+1/4+...+1/200)`
`=(1+1/2+1/3+1/4+...+1/199+1/200)-2( 1/2+1/4+...+1/200)`
`=1/101+1/102+....+1/200`
$\\$
`B=1/(101.200)+1/(102.199)+....+1/(200.101)`
`=1/301.(301/(101.200)+301/(102.199)+...+301/(200.101))`
`=1/301 .(1/200+1/101+1/199+1/102+...+1/101+1/200)`
`=1/301.2(1/101+1/102+...+1/200)`
`=2/301.(1/101+1/102+...+1/200)`
`=> A/B=\frac{\frac{1}{101} + \frac{1}{102} + ... + \frac{1}{200}}{\frac{2}{301} ( \frac{1}{101} + \frac{1}{102} + ... + \frac{1}{200})}=301/2`
