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From module Telescoping Sums and Products
What is the value of the product (1⋅32⋅2)(2⋅43⋅3)(3⋅54⋅4)⋯(97⋅9998⋅98)(98⋅10099⋅99)(\frac{1 \cdot 3}{2 \cdot 2})(\frac{2 \cdot 4}{3 \cdot 3})(\frac{3 \cdot 5}{4 \cdot 4}) \cdots (\frac{97 \cdot 99}{98 \cdot 98})(\frac{98 \cdot 100}{99 \cdot 99})(2⋅21⋅3)(3⋅32⋅4)(4⋅43⋅5)⋯(98⋅9897⋅99)(99⋅9998⋅100)?
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