1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+.1/(x+2011)(x+2012)=1/2x+4024

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1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+.1/(x+2011)(x+2012)=1/2x+40241/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3

1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+.1/(x+2011)(x+2012)=1/2x+4024
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+.1/(x+2011)(x+2012)=1/2x+4024

1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+.1/(x+2011)(x+2012)=1/2x+4024
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+2011) -1/(x+2012)=1/2(x+2012)
1/(x+1)-1/(x+2012)=1/2(x+2012)
1/(x+1)=3/2(x+2012)
2x+2014=3x+3
x=2011