Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2006 AMC 8 Problems/Problem 9

Revision as of 20:51, 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)}\...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2006_AMC_8_Problems/Problem_9&oldid=42178"