Difference between revisions of "2006 AMC 8 Problems/Problem 9"

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== Solution ==
 
== Solution ==
 
By telescoping, it's easy to see the sum becomes <math> \frac{2006}{2}=\boxed{\textbf{(C)}\ 1003} </math>.
 
By telescoping, it's easy to see the sum becomes <math> \frac{2006}{2}=\boxed{\textbf{(C)}\ 1003} </math>.
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{{AMC8 box|year=2006|num-b=8|num-a=10}}

Revision as of 14:57, 21 November 2011

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 $\frac{2006}{2}=\boxed{\textbf{(C)}\ 1003}$.

2006 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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All AJHSME/AMC 8 Problems and Solutions