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2008 AMC 10AProblem 5P1-10~1 minPrint
Algebraic ManipulationSequences & SeriesCollapse a sum or product by cancellation

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

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2008 12A #4.