# First Problem in 2016

$\displaystyle\sum_{k=2}^{\infty}0.\overline{01}_{k}=S_{4}$

If $$S=\dfrac{p}{q}$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q$$.

Note: $$S_{4}$$ represents $$S$$ written in base 4.

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