2008 AMC 12A Problem 4

Problem 4 of 25EasierAlgebra

Which of the following is equal to the product

\begin{aligned} &\dfrac{8}{4} \cdot \dfrac{12}{8} \cdot \dfrac{16}{12} \\ &\quad \cdots \dfrac{4n + 4}{4n} \cdots \dfrac{2008}{2004}? \end{aligned}

Show solution

Solution

Every denominator except the first cancels with the numerator of the preceding fraction, so the product collapses to

\dfrac{2008}{4} = 502.

Thus, B is the correct answer.

Concepts: telescoping

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.