2006 AMC 8 Problems/Problem 9

Problem

What is the product of $\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdots\times\frac{2006}{2005}$ ?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 1002\qquad\textbf{(C)}\ 1003\qquad\textbf{(D)}\ 2005\qquad\textbf{(E)}\ 2006$

Solution

After looking at the problem, we immediately notice that terms cancel out, leaving us with $\frac{2006}{2}=\boxed{\textbf{(C)}\ 1003}$ . And that is the answer.

2006 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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All AJHSME/AMC 8 Problems and Solutions

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2006 AMC 8 Problems/Problem 9

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