Đáp án:
`A= 49/200`
`B= 33/100`
`C=50/101`
Giải thích các bước giải:
`A = 1/(4.5) + 1/(5.6) + ... + 1/(199 . 200)`
`-> A= 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/199 - 1/200`
`-> A = 1/4 + (-1/5 + 1/5) + ... +(-1/199 + 1/199 ) - 1/200`
`-> A = 1/4 - 1/200`
`-> A=50/200 - 1/200`
`-> A = 49/200`
Vậy `A=49/200`
`B = 3/(3.6) + 3/(6.9) + ... + 3/(297.300)`
`-> B = 1/3 - 1/6 + 1/6 - 1/9 + ... + 1/297 - 1/300`
`-> B = 1/3 + (-1/6 + 1/6) + ... + (-1/297 + 1/297) - 1/300`
`-> B = 1/3 - 1/300`
`-> B = 100/300 - 1/300`
`->B=33/100`
Vậy `B=33/100`
`C = 2/(1.5) + 2/(5.9) + ... + 2/(97 . 101)`
`-> 2C = 4/(1.5) + 4/(5.9) + ... + 4/(97 . 101)`
`-> 2C = 1 -1/5 + 1/5 - 1/9 + ... + 1/97 - 1/101`
`->2C=1+ (-1/5 + 1/5) + ... +(-1/97 + 1/97) - 1/101`
`->2C=1-1/101`
`->2C=101/101 - 1/101`
`->2C=100/101`
`->C=100/101 : 2`
`->C=50/101`
Vậy `C=50/101`
