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+1/2×3+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+1/2×3+1/3×4+……+1/98×99+1/99×100
=1-½+½-1/3+1/3-1/4+······+1/99-1/100
=1-1/100
=99/100

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