Which of the following is equal to the product &(8)/(4) × (12)/(8) × (16)/(12) & … (4n + 4)/(4n) … (2008)/(2004)?

2008 AMC 12A Problem 4

Attempt Problem 4 of the 2008 AMC 12A 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 2008 AMC 12A solutions, or check the answer key.

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

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}

251

502

1004

2008

4016

Each denominator cancels with the numerator of the previous fraction

Only the last numerator and the first denominator survive

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.