Question

简算1÷（1×2×3）+1÷（2×3×4）+1÷（3×4×5）+1÷（4×5×6）+.+1÷（98×99×100）

Answer 1

=(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