trước tiên bạn phải tính:

2013/1+2012/2+2011/3+.....+2/2012+1/2013

=1+2012/2)+(1+2011/3)+.....+(1+2/2012)+(1+1/2013) +1 {BƯỚC NÀY TÁCH 2013 RA LÀM 2013SỐ1 ĐỂ CÔNG VS CÁC THỪA SỐ CÒN LẠI}

=2014/2+2014/3+...+2014/2012+2014/2013+2014/2014

=2014.(1/2+1/3+....+1/2012+1/20131/2014

suy ra x=2014

\(\dfrac{x-1}{2014}+\dfrac{x-2}{2013}=\dfrac{x-3}{2012}+\dfrac{x-4}{2011}\)

\(\Leftrightarrow\text{​​}\text{​​}\text{​​}\dfrac{x-1}{2014}-1+\dfrac{x-2}{2013}-1=\dfrac{x-3}{2012}-1+\dfrac{x-4}{2011}-1\)

\(\Leftrightarrow\dfrac{x-2015}{2014}+\dfrac{x-2015}{2013}-\dfrac{x-2015}{2012}-\dfrac{x-2015}{2011}=0\)

\(\Leftrightarrow\left(x-2015\right)\left(\dfrac{1}{2014}+\dfrac{1}{2013}-\dfrac{1}{2012}-\dfrac{1}{2011}\right)=0\)

mà \(\dfrac{1}{2014}+\dfrac{1}{2013}-\dfrac{1}{2012}-\dfrac{1}{2011}\ne0\)

nên \(x-2015=0\)

\(\Leftrightarrow x=2015\)

x+1/2014 + x+2/2013 = x+3/2012 + x+4/2011

=> x+1/2014 + 1 + x+2/2013 + 1 = x+3/2012 + 1 + x+4/2011 + 1

=> x+2015/2014 + x+2015/2013 = x+2015/2012 + x+2015/2011

=> x+2015/2012 + x+2015/2011 - x+2015/2013 - x+2015/2014 = 0

=> (x + 2015).(1/2012 + 1/2011 - 1/2013 - 1/2014) = 0

Vì 1/2011 > 1/2013; 1/2012 > 1/2014

=> 1/2012 + 1/2011 - 1/2013 - 1/2014 khác 0

=> x + 2015 = 0

=> x = -2015

bấm vào chữ xanh này nha bn : /hoi-dap/question/113985.html

(x + 4)/2010 + (x+3)/2011 = (x+2)/2012 + (x+1)/2013 

<=> [(x + 4)/2010 + 1] + [(x+3)/2011 + 1] = [(x+2)/2012 + 1] + [(x+1)/2013 + 1] 

<=> (x + 2014)/2010 + (x + 2014)/2011 = (x + 2014)/2012 + (x + 2014)/2013 

<=> (x + 2014)/2010 + (x + 2014)/2011 - (x + 2014)/2012 - (x + 2014)/2013 = 0 

<=> (x + 2014).(1/2010 + 1/2011 - 1/2012 - 1/2013) = 0 

Ta thấy (1/2010 + 1/2011 - 1/2012 - 1/2013) ≠ 0 

Vậy suy ra x = -2014

đúng ko các bạn 

chac the

\(\dfrac{x-1}{2013}+\dfrac{x-2}{2012}+\dfrac{x-3}{2011}=\dfrac{x-4}{2010}+\dfrac{x-5}{2009}+\dfrac{x-6}{2008}\)

\(\Leftrightarrow\dfrac{x-1}{2013}-1+\dfrac{x-2}{2012}-1+\dfrac{x-3}{2011}-1=\dfrac{x-4}{2010}-1+\dfrac{x-5}{2009}-1+\dfrac{x-6}{2008}-1\)

=>x-2014=0

hay x=2014

ủng hộ mình lên 280 điểm với các bạn

x+1/2013+1+x+2/2012+1=x+3/2011+1+x+4/2010+1

x+1+2013/2013+x+2+2012/2012=x+3+2011/2011+x+4+2010/2010

x+2014/2013+x+2014/2012-x+2014/2011-x+2014/2010=0

(x+2014)(1/2013+1/2012-1/2011-1/2010)=0

x+2014=0

x=-2014

\(\frac{x+1}{2013}+1+\frac{x+2}{2012}+1=\frac{x+3}{2011}+1+\frac{x+4}{2010}+1\)

\(\Rightarrow\frac{x+2014}{2013}+\frac{x+2014}{2012}=\frac{x+2014}{2011}+\frac{x+2014}{2010}\)

\(\Rightarrow\left(x+2014\right)\left(\frac{1}{2013}+\frac{1}{2012}-\frac{1}{2011}-\frac{1}{2010}\right)=0\)

\(\Rightarrow\left(x+2014\right)=0\)

\(\Rightarrow x=-2014\)