观察下面的变形规律1/(1×2)=1-1/2；1/(2×3)=1/2-1/3；1/(3×4)=1/3-1/4.

题目

观察下面的变形规律1/(1×2)=1-1/2；1/(2×3)=1/2-1/3；1/(3×4)=1/3-1/4.
求
1/(1×2)+1/(2×3)+1/(3×4）+……+1/(2011×2012)·

答案

1/1*2+1/2*3+1/3*4+...+1/n（n+1）=
=1-1/2+1/2-1/3+...+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
所以是2011/2012