1/2×1+1/2×3+1/3×4=1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4
(1)猜想并写出1/n(n+1)=1/n - 1/(n+1)
(2)直接写出下列各式的计算结果:
1、1/1×2+1/2×3+1/3×4…+1/2006×2007=1-1/2007=2006/2007
2、1/1×2+1/2×3+1/3×4+…1/n(n+1)=1- 1/(n+1)
(3)探究并计算:
1/2×4+1/4×6+1/6×8+…1/2006×2008
=½x(1/2-1/4)+½x(1/4-1/6)+……+½x(1/2006-1/2008)
=½x(1/2-1/4+1/4-1/6+……+1/2006-1/2008)
=½x(1/2-1/2008)
=½x(1003/2008)
=1003/4016