1/2+1/6+1/12+1/20+1/x(x+1)=2011/2012
1-1/2+1/2-1/3+1/3-1/4+……+1/x-1/(x+1)=2011/2012
1-1/(x+1)=2011/2012
1-2011/2012=1/(x+1)
x+1=2012
x=2011