AMC 8 2019 Problem 17

What is the value of the product $$\left(\frac{1\cdot3}{2\cdot2}\right)\left(\frac{2\cdot4}{3\cdot3}\right)\left(\frac{3\cdot5}{4\cdot4}\right)\cdots\left(\frac{97\cdot99}{98\cdot98}\right)\left(\frac{98\cdot100}{99\cdot99}\right)?$$ $\textbf{(A) }\frac{1}{2} \textbf{(B) }\frac{50}{99} \textbf{(C) }\frac{9800}{9801} \textbf{(D) }\frac{100}{99} \textbf{(E) }50$