# No no Please not Double Factorials

Number Theory Level 4

Define $$n!!$$ as the double factorial. If $$\displaystyle\sum_{i=1}^{2009} \frac{(2i-1)!!}{(2i)!!}$$ is expressed as a fraction in lowest terms, its denominator is $$2^ab$$ with $$b$$ odd. Find $$\dfrac{ab}{10}$$.

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