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2008 AMC 10A Problem 5

Problem 5 of 25EasierAlgebraArithmetic

Which of the following is equal to the product 84⋅128⋅1612⋯4n+44n⋯20082004? \begin{aligned} &\dfrac{8}{4} \cdot \dfrac{12}{8} \cdot \dfrac{16}{12} \cdots \dfrac{4n+4}{4n} \\ &\quad \cdots \dfrac{2008}{2004}? \end{aligned}

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Solution

Every denominator except the first cancels with the numerator of the previous fraction, so the whole product telescopes to 20084=502.\dfrac{2008}{4} = 502. Thus, the correct answer is B.
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Tagged: telescoping · fraction

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