原式=1/1×2-1/1×2+1/2×3+1/3×4+1/4×5+.+1/98×99+1/99×100
=1/1×2+1/2×3+1/3×4+1/4×5+.+1/98×99+1/99×100-1/1×2
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+-----+1/98-1/99+1/99-1/100-1/1×2
=1-1/100-1/1×2
=99/100-2
=-101/100
原式=1/1×2-1/1×2+1/2×3+1/3×4+1/4×5+.+1/98×99+1/99×100
=1/1×2+1/2×3+1/3×4+1/4×5+.+1/98×99+1/99×100-1/1×2
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+-----+1/98-1/99+1/99-1/100-1/1×2
=1-1/100-1/1×2
=99/100-2
=-101/100