Đáp án:

Giải thích các bước giải:

`a)`

` A = - 2/3 + 3/4 - (- 1)/6 + (- 2)/5 `

` A = - 2/3 + 3/4 + 1/6 - 2/5 `

` A = ( - 2/3 + 1/6 ) + ( 3/4 - 2/5 ) `

` A = - 1/2 + 7/20 `

` A = - 3/20 `

``

`b)`

` (- 2)/3 + (- 1)/5 + 3/4 - 5/6 - (- 7)/10 `

`= - 2/3 - 1/5 + 3/4 - 5/6 + 7/10 `

`= ( - 2/3 - 5/6 ) + ( - 1/5 + 7/10 + 3/4 ) `

`= - 3/2 + 5/4 `

`= - 1/4 `

``

`c)`

` 1/2 - (- 2)/5 + 1/3 + 5/7 - (- 1)/6 + (- 4)/35 + 1/41 `

`= 1/2 + 2/5 + 1/3 + 5/7 + 1/6 - 4/35 + 1/41 `

`= ( 1/2 + 1/3 + 1/6 ) + ( 2/5 + 5/7 - 4/35 ) + 1/41 `

`= 1 + 1 + 1/41 `

`= 2 + 1/41 `

`= 83/41 `

``

`d)`

` D = 1/(100 * 99) - 1/(99 * 98) - 1/(98 * 97) - ....... - 1/(3 * 2) - 1/(2 * 1) `

` D = 1/9900 - ( 1/(99 * 98) + 1/(98 * 97) + ...... + 1/(3 * 2) + 1/(2 * 1) ) `

` D = 1/9900 - ( 1/(1 * 2) + 1/(2 * 3) + ...... + 1/(97 * 98) + 1/(98 * 99) ) `

` D = 1/9900 - ( 1 - 1/2 + 1/2 - 1/3 + ........ + 1/97 - 1/98 + 1/98 - 1/99 ) `

` D = 1/9900 - ( 1 - 1/99 ) `

` D = 1/9900 - 98/99 `

` D = - 9799/9900 `

Vậy ` D = - 9799/9900`