a) `(1 - 1/2) xx (1 - 1/3) xx (1 - 1/4) xx (1 - 1/5)`

`= 1/2 xx 2/3 xx 3/4 xx 4/5`

`= 1/cancel2 xxcancel2/cancel3 xx cancel3/cancel4 xx cancel4/5`

`= 1/5`

b) `2000/2001 xx 2002/2003 xx 2001/2002 xx 2003/2004 xx 2006/2003`

`= (2000 xx  2002 xx 2001 xx 2003 xx 2006)/(2001 xx 2003 xx 2002 xx 2004 xx 2003)`

`= (2000 xx  cancel2002 xx cancel2001 xx cancel2003 xx 2006)/(cancel2001 xx 2003 xx cancel2002 xx 2004 xx cancel2003)`

`= 2000/2003 xx 2006/2004`

c) `5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90`

`= (1 - 1/6) + (1 - 1/12) + (1 - 1/20) + (1 - 1/30) + (1 - 1/42) + (1 - 1/56) + (1 - 1/72) + (1 - 1/90)`

`= 8 - (1/6 - 1/12 - 1/20 - 1/30 - 1/42 - 1/56 - 1/72 - 1/90)`

`= 8 - (1/(2 xx 3) + 1/(3 xx 4) + 1/(4 xx 5) + 1/(5 xx 6) + 1/(6 xx 7) + 1/(7 xx 8) + 1/(8 xx 9) + 1/(9 xx 10))`

`= 8 - (1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10)`

`= 8 - (1/2 - 1/10)`

`= 8 - (5/10 - 1/10)`

`= 8 - 4/10`

`= 80/10 - 4/10`

`= 76/10 = 38/5`

Đáp án+Giải thích các bước giải:

a)`(1-1/2)xx(1-1/3)xx(1-1/4)xx(1-1/5)`

`=1/2xx2/3xx3/4xx4/5`

`=(1xx2xx3xx4)/(2xx3xx4xx5)`

`=1/5`

b) `2000/2001xx2002/2003xx2001/2002xx2003/2004xx2006/2003`

`=(2000xx2002xx2001xx2003xx2006)/(2001xx2003xx2002xx2004xx2003)`

`=(2000xx2006)/(2004xx2003)` 

c) `5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90`

`=(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+(1-1/42)+(1-1/56)+(1-1/72)+(1-1/90)`

`=8-(1/6-1/12-1/20-1/30-1/42-1/56-1/72-1/90)`

`=8-(1/(2xx3)+1/(3xx4)+1/(4xx5)+1/(5xx6)+1/(6xx7)+1/(7xx8)+1/(8xx9)+1/(9xx10)`

`=8-(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)`

`=8-(1/2-1/10)`

`=8-2/5`

`=38/5`