Q200
ArithmeticAlgebra, Equations & Operations
The simplified value of $\left(2 - \frac{1}{3}\right)\left(2 - \frac{3}{5}\right)\left(2 - \frac{5}{7}\right) \cdots \left(2 - \frac{997}{999}\right)$ is
- a.$\frac{5}{999}$
- b.$\frac{1001}{999}$
- c.$\frac{1001}{3}$
- d.$\frac{501}{999}$
Answer: (C) $\frac{1001}{3}$
Each factor simplifies: $2 - \frac{1}{3} = \frac{5}{3}$, $2 - \frac{3}{5} = \frac{7}{5}$, …, $2 - \frac{997}{999} = \frac{1001}{999}$. In the product $\frac{5}{3} \times \frac{7}{5} \times \cdots \times \frac{1001}{999}$ every numerator cancels the next denominator, leaving $\frac{1001}{3}$. Option B is just the last factor.