# Binomial coefficients in the denominator!

If the value of the sum

$\displaystyle\sum_{r=0}^{1006} \frac{2012-2r}{(r+1)\dbinom{2013}{r+1}}$

is $$S$$ then find the value of $$S+\frac{\displaystyle1}{\dbinom{2013}{1006}}$$.

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