2008 AMC 12A Problems/Problem 4

Problem

Which of the following is equal to the product

$\frac {8}{4}\cdot\frac {12}{8}\cdot\frac {16}{12}\cdots\frac {4n + 4}{4n}\cdots\frac {2008}{2004}$ ?

$\textbf{(A)}\ 251 \qquad \textbf{(B)}\ 502 \qquad \textbf{(C)}\ 1004 \qquad \textbf{(D)}\ 2008 \qquad \textbf{(E)}\ 4016$

Solution

$\frac {8}{4}\cdot\frac {12}{8}\cdot\frac {16}{12}\cdots\frac {4n + 4}{4n}\cdots\frac {2008}{2004} = \frac {1}{4}\cdot\left(\frac {8}{8}\cdot\frac {12}{12}\cdots\frac {4n}{4n}\cdots\frac {2004}{2004}\right)\cdot 2008 = \frac{2008}{4} =$ $502 \Rightarrow B$ .

2008 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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2008 AMC 12A Problems/Problem 4

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