Đáp án:

Giải thích các bước giải:

 Bài `3`

`a)A=4/(3xx7) +4/(7xx11) + 4/(11xx15) + 4/(15xx19) +4/(19xx23) + 4/(23xx27)`

`A=1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+1/19-1/23+1/23-1/27`

`A=1/3-1/27`

`A=9/27 - 1/27`

`A=8/27`

Vậy `a=8/27`

`b)B=2/(1xx3) +2/(3xx5) +2/(5xx7) +2/(7xx9) + 2/(9xx11) +2/(11xx13)`

`B=1/1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13`

`B=1-1/13`

`B=12/13`

Vậy `B=12/13`

`c)C=1/(1xx3) +1/(3xx5) +1/(5xx7) + .... + 1/(99xx101)`

`C=1/2(2/(1xx3)  + 2/(3xx5) +2/(5xx7) + .... +2/(99xx101))`

`C=1/2(1/1-1/3+1/3-1/5+1/5-1/7 + ... +1/99-1/101)`

`C=1/2(1-1/101)`

`C=100/101`

`C=50/101`

Vậy `C=50/101`

`d)D=2/(1xx2) +2/(2xx3) +2/(3xx4) + ... +2/(99xx100)`

`D=2(1/(1xx2) +1/(2xx3) +1/(3xx4) + ... +1/(99xx100))`

`D=2(1/1-1/2+1/2-1/3+1/3-1/4 + ... +1/99-1/100)`

`D=2(1-1/100)`

`D=2*99/100`

`D=99/50`

Vậy `D=99/50`