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2006 AMC 8 Problems/Problem 9

Revision as of 19:51, 6 September 2011 by Math Kirby (talk | contribs) (Created page with "== Problem == What is the product of <math> \frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdots\times\frac{2006}{2005} </math> ? <math> \textbf{(A)}\ 1\qquad\textbf{(B)}\...")
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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

By telescoping, it's easy to see the sum becomes $\frac{2006}{2}=\boxed{\textbf{(C)}\ 1003}$.

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