觀察下麵的變形規律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)·

觀察下麵的變形規律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)·

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