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MAA AMC
AMC 8
2019 AMC 8
17
17
Part of
2019 AMC 8
Problems
(1)
Telescoping Product
Source: 2019 AMC 8 #17
11/19/2019
What is the value of the product
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\left(\frac{1\cdot3}{2\cdot2}\right)\left(\frac{2\cdot4}{3\cdot3}\right)\left(\frac{3\cdot5}{4\cdot4}\right)\cdots\left(\frac{97\cdot99}{98\cdot98}\right)\left(\frac{98\cdot100}{99\cdot99}\right)?
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<span class='latex-bold'>(A) </span>\frac{1}{2}\qquad<span class='latex-bold'>(B) </span>\frac{50}{99}\qquad<span class='latex-bold'>(C) </span>\frac{9800}{9801}\qquad<span class='latex-bold'>(D) </span>\frac{100}{99}\qquad<span class='latex-bold'>(E) </span> 50
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