1 1 1 1 ------ + ------ + ------ + .+ -------------- = 1×2 2×3 3×4 2009×2010 1 1 1 1 ---------- + --------- + ---------- + .+ -----------= 10×16 16×22 22×28 94×100

1 1 1 1 ------ + ------ + ------ + .+ -------------- = 1×2 2×3 3×4 2009×2010 1 1 1 1 ---------- + --------- + ---------- + .+ -----------= 10×16 16×22 22×28 94×100

1 1 1 1
------ + ------ + ------ + .+ --------------
1×2 2×3 3×4 2009×2010
=1-1/2+1/2-1/3+1/3-1/4+…… +1/2009-1/2010
=1-1/2010=2009/2010
two