1959 AHSME Problems/Problem 37

Problem

When simplified the product $\left(1-\frac13\right)\left(1-\frac14\right)\left(1-\frac15\right)\cdots\left(1-\frac1n\right)$ becomes: $\textbf{(A)}\ \frac1n \qquad\textbf{(B)}\ \frac2n\qquad\textbf{(C)}\ \frac{2(n-1)}{n}\qquad\textbf{(D)}\ \frac{2}{n(n+1)}\qquad\textbf{(E)}\ \frac{3}{n(n+1)}$

Solution

The product $\left(1-\frac13\right)\left(1-\frac14\right)\left(1-\frac15\right)\cdots\left(1-\frac1n\right)$ can be simplified to $\frac{2*3*4\cdots*(n-2)*(n-1)}{3*4*5\cdots*(n-1)*n}$ , which, through telescoping, ultimately works out to $\boxed{\textbf{(B) }\frac{2}{n}}$ .

1959 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 36	Followed by Problem 38
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1959 AHSME Problems/Problem 37

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