2006 AMC 8 Problem 9 — Solution | LIVE by Po-Shen Loh

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2006 AMC 8 Problem 9

Attempt Problem 9 of the 2006 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

9.

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

$1$

$1002$

$1003$

$2005$

$2006$

Answer: C

Concepts:telescoping

Difficulty rating: 1130

Solution:

Note that the numerator of every fraction cancels with the denominator of the following fraction. This leaves two numbers: $\dfrac{2006}{2} = 1003.$

Thus, C is the correct answer.

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