MathDB
Telescoping Product

Source: 2019 AMC 8 #17

November 19, 2019

Problem Statement

What is the value of the product (1⋅32⋅2)(2⋅43⋅3)(3⋅54⋅4)⋯(97⋅9998⋅98)(98⋅10099⋅99)?\left(\frac{1\cdot3}{2\cdot2}\right)\left(\frac{2\cdot4}{3\cdot3}\right)\left(\frac{3\cdot5}{4\cdot4}\right)\cdots\left(\frac{97\cdot99}{98\cdot98}\right)\left(\frac{98\cdot100}{99\cdot99}\right)?
<spanclass=′latex−bold′>(A)</span>12<spanclass=′latex−bold′>(B)</span>5099<spanclass=′latex−bold′>(C)</span>98009801<spanclass=′latex−bold′>(D)</span>10099<spanclass=′latex−bold′>(E)</span>50<span class='latex-bold'>(A) </span>\frac{1}{2}\qquad<span class='latex-bold'>(B) </span>\frac{50}{99}\qquad<span class='latex-bold'>(C) </span>\frac{9800}{9801}\qquad<span class='latex-bold'>(D) </span>\frac{100}{99}\qquad<span class='latex-bold'>(E) </span> 50
Back to ProblemsView on AoPS