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Bạn tham khảo bài.

Câu `1.`

`x=1/(2013.2012)-1/(2012.2011)-...-1/(3.2)-1/(2.1)`

`->x=1/(2013.2012)-(1/(1.2)+1/(2.3)+...+1/(2011.2012))`

`->x=1/(2013.2012)-(1-1/2+1/2-1/3+...+1/2011-1/2012)`

`->x=1/(2013.2012)-(1 - 1/2012)`

`->x = 1/(2013 . 2012) - 2011/2012`

`->x=1/(2013.2012)-(2013.2011)/(2013.2012)`

`->x=(1 - 2013.2011)/(2013.2012)`

Vậy `x=(1 - 2013.2011)/(2013.2012)`

Câu `2.`

`x-20/(11.13)-... - 20/(53.55)=(-3)/11`

`->x-(20/(11.13)+...+20/(53.55))=(-3)/11`

`->x-20 (1/(11.13)+...+1/(53.55))=(-3)/11`

`->x - 20 . 1/2 . (1/11-1/13+...+1/53-1/55)=(-3)/11`

`->x - 10 . (1/11-1/55)=(-3)/11`

`->x-10 . 4/55=(-3)/11`

`->x-8/11=(-3)/11`

`->x=5/11`

Vậy `x=5/11`

Đáp án:

Giải thích các bước giải:

`1.`

`x =1/{2013·2012}-1/{2012·2011}-1/{2011·2010}-......-1/{3·2}-1/{2·1}`

`x = 1/{2013·2012} - (1/{1·2}+1/{2·3}+...+1/{2010·2011}+1/{2011·2012})`

`x = 1/{2013·2012} - (1 - 1/2+ 1/2 - 1/3 +...+ 1/2010 - 1/2011 + 1/2011 - 1/2012)`

`x = 1/{2013·2012} - 2011/2012`

`x = 1/{2013·2012 } - {2011 · 2013}/{2012·2013}`

`x = -{2011 · 2013 + 1}/{2012·2013}`

`2.`

`x-20/11.13-20/13.15 -1/15.17-.....-20/53.55=-3/11`

`x - (20/11.13-20/13.15 -1/15.17-.....-20/53.55) =-3/11`

`x - 10(1/11 - 1/13 + 1/13 - 1/15 + 1/15 - 1/17 +...+ 1/53 - 1/55) =-3/11`

`x - 10(1/11 - 1/55) =-3/11`

`x - 8/11 = -3/11`

`x = -3/11 + 8/11`

`x = 5/11`