CAYLEY 2024 Problem 16

Suppose that \sqrt{\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \cdots \times \frac{n-1}{n}}=\frac{1}{8}. (The expression under the square root is the product of n-1 fractions.) The value of n is

Answer Choices
A. 81
B. 64
C. 16
D. 256
E. 100