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

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