1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
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1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100)
=(1-1/100)
=99/100
1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
1/1×2+1/2×3+1/3×4+.+1/98×99+1/99×100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/98-1/99)+(1/99-1/100)
=(1-1/100)
=99/100