10.74 Simplify $\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right) \cdots\left(1-\frac{1}{n}\right)$ to get
(A) $\frac{1}{n}$.
(B) $\frac{2}{n}$.
(C) $\frac{2(n-1)}{n}$.
(D) $\frac{2}{n(n+1)}$.
(E) $\frac{3}{n(n+1)}$.
(10th American High School Mathematics Examination, 1959)
[Solution] Original expression $=\frac{2}{3} \cdot \frac{3}{4} \cdot \frac{4}{5} \cdot \cdots \cdot \frac{n-2}{n-1} \cdot \frac{n-1}{n}=\frac{2}{n}$. Therefore, the answer is $(B)$.