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