2006 AMC 8 Problems/Problem 9: Difference between revisions

Revision as of 19:00, 24 December 2012

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

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

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

2006 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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