Đáp án+Giải thích các bước giải:
`A=1/1.2+1/2.3+1/3.4+...+1/2003.2004`
`=1-1/2+1/2-1/3+1/3-1/4+...+1/2003-1/2004`
`=1-1/2004`
`=2004/2004-1/2004`
`=2003/2004`
Vậy `A=2003/2004`
`B=1/18+1/54+1/108+...+1/990`
`=1/(3).(3/18+3/54+3/108+...+3/990)`
`=1/(3).(3/3.6+3/6.9+3/9.12+...+3/30.33)`
`=1/(3).(1/3-1/6+1/6-1/9+1/9-1/12+...+1/30-1/33)`
`=1/(3).(1/3-1/33)`
`=1/(3).(11/33-1/33)`
`=1/(3).(10)/33`
`=10/99`
Vậy `B=10/99`