Mình k hiểu dạng toán này mong chỉ giáo ạ

`a)`

`3/(2xx5) + 3/(5xx8) + 3/(8xx11) + ... + 3/(47xx50) + 3/(50xx53)`

`= 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + ... + 1/47 - 1/50 + 1/50 - 1/53`

`= 1/2 - 1/53`

`= 53/106 - 2/106`

`= 51/106`

`b)`

`4/(3xx5) + 4/(5xx7) + 4/(7xx9) + ... + 4/(25xx27) + 4/(27xx29)`

`= 2 xx (2/(3xx5) + 2/(5xx7) + 2/(7xx9) + ... + 2/(25xx27) + 2/(27xx29))`

`= 2 xx (1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/25 - 1/27 + 1/27 - 1/29)`

`= 2 xx (1/3 - 1/29)`

`= 2 xx (29/87 - 3/87)`

`= 2 xx 26/87`

`= 52/87`

`c)`

`2/(1xx4) + 2/(4xx7) + 2/(7xx10) + ... + 2/(31xx34) + 2/(34xx37)`

`= 2/3 xx (3/(1xx4) + 3/(4xx7) + 3/(7xx10) + ... + 3/(31xx34) + 3/(34xx37))`

`= 2/3 xx (1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/31 - 1/34 + 1/34 - 1/37)`

`= 2/3 xx (1 - 1/37)`

`= 2/3 xx 36/37`

`= 24/37`

`d)`
`2/3 + 2/15 + 2/35 + ... + 2/399 + 2/483`
`= 2/(1xx3) + 2/(3xx5) + 2/(5xx7) + ... + 2/(19xx21) + 2/(21xx23)`
`= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/19 - 1/21 + 1/21 - 1/23`
`= 1 - 1/23`
`= 22/23`