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Odd/Even Factorial Division

Source: AIME 2009II Problem 7

April 2, 2009
factorialAMCAIMEfloor functionfunction

Problem Statement

Define n!! n!! to be n(n\minus{}2)(n\minus{}4)\ldots3\cdot1 for n n odd and n(n\minus{}2)(n\minus{}4)\ldots4\cdot2 for n n even. When \displaystyle \sum_{i\equal{}1}^{2009} \frac{(2i\minus{}1)!!}{(2i)!!} is expressed as a fraction in lowest terms, its denominator is 2ab 2^ab with b b odd. Find ab10 \displaystyle \frac{ab}{10}.
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