Đáp án + Giải thích các bước giải:

`1991/1990 xx 1992/1991 xx 1993/1992 xx 1994/1993 xx 995/997`

`= (1991/1990 xx 1992/1991) xx (1993/1992 xx 1994/1993) xx 995/997`

`= 1992/1990 xx 1994/1992 xx 995/997`

`= 1994/1990 xx 995/997`

`= 2/2`

`= 1` 

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`2/(1 xx 2) + 2/(2 xx 3) + 2/(3 xx 4) + 2/(4 xx 5) + 2/(5 xx 6)`

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

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

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

`= 2 xx (1 - 1/6)`

`= 2 xx 5/6`

`= 5/3`

Đáp án:

`b) 1991/1990 xx 1992/1991 xx 1993/1992 xx 1994/1993 xx 995/997`

`= 1991/(995xx2) xx 1992/1991 xx 1993/1992 xx (997xx2)/1993 xx 995/997`

`= (1991xx1992xx1993xx997xx2xx995)/(995xx2xx1991xx1992xx1993xx997)`

`= (\cancel{1991}xx\cancel{1992}xx\cancel{1993}xx\cancel{997}xx\cancel{2}xx\cancel{995})/(\cancel{995}xx\cancel{2}xx\cancel{1991}xx\cancel{1992}xx\cancel{1993}xx\cancel{997}`

`= 1`
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`c) 2/(1xx2) + 2/(2xx3) + 2/(3xx4) + 2/(4xx5) + 2/(5xx6)`

`= 2 . (1/(1xx2) + 1/(2xx3) + 1/(3xx4) + 1/(4xx5) + 1/(5xx6))`

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

`= 2 . (1 - 1/6)`

`= 2 . 5/6`

`= 5/3`

Giải thích các bước giải: