=(1/2)(1/1×2-1/2×3)+(1/2)(1/2×3-1/3×4)+……+(1/2)(1/98×99-1/99×100)
=(1/2)(1/1×2-1/2×3+1/2×3-1/3×4+……+1/98×99-1/99×100)
=(1/2)(1/1×2-1/99×100)
=4949/19800