解
x/(1×2)+x/(2×3)+……+x/(2012×2013)=2012
x[1/(1×2)+1/(2×3)+……+1/(2012×2013)]=2012
x[(1-1/2)+(1/2-1/3)+……+(1/2012-1/2013)]=2012
x[1+(1/2-1/2)+(1/3-1/3)+……(1/2012-1/2012)-1/2013]=2012
x(1-1/2013)=2012
2012x/2013=2012
∴x=2013
解
x/(1×2)+x/(2×3)+……+x/(2012×2013)=2012
x[1/(1×2)+1/(2×3)+……+1/(2012×2013)]=2012
x[(1-1/2)+(1/2-1/3)+……+(1/2012-1/2013)]=2012
x[1+(1/2-1/2)+(1/3-1/3)+……(1/2012-1/2012)-1/2013]=2012
x(1-1/2013)=2012
2012x/2013=2012
∴x=2013