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1/1×2×3+1/2×3×4+1/3×4×5+1/4×5×6……+1/98×99×100
=1/2×(1/1×2-1/2×3)+1/2×(1/2×3-1/3×4)+1/2×(1/3×4-1/4×5)+1/2×(1/4×5-1/5×6)+……+1/2×(1/98×99-1/99×100)
=1/2×(1/1×2-1/2×3+1/2×3-1/3×4+1/3×4-1/4×5+1/4×5-1/5×6+……＋1/98×99-1/99×100)
=1/2×(1/1×2-1/99×100)
=4949/19800
=1/2×(1/1×2-1/2×3)+1/2×(1/2×3-1/3×4)+1/2×(1/3×4-1/4×5)+1/2×(1/4×5-1/5×6)+……+1/2×(1/98×99-1/99×100)
=1/2×(1/1×2-1/2×3+1/2×3-1/3×4+1/3×4-1/4×5+1/4×5-1/5×6+……＋1/98×99-1/99×100)
=1/2×(1/1×2-1/99×100)
=4949/19800
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