What is the value of the product $(\frac{1\cdot 3}{2\cdot 2})(\frac{2\cdot 4}{3\cdot 3})(\frac{3\cdot 5}{4\cdot 4})\cdots (\frac{47\cdot 49}{48\cdot 48})(\frac{48\cdot 50}{49\cdot 49})$?