1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)

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1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
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1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)

1/(1×2)+1/(2×3)+1/(3×4)+⋯+1/(99×100)
=1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100
(1/(1*2)=1-1/2,1/(2*3)=1/2-1/3,……）

原式=1-1/2+1/2-1/3+...+1/99-1/100
=1-1/100
=99/100