# I Thought These Were Partial Fractions

Algebra Level 5

If $$x_{1},x_{2},.....,x_{71}$$ satisfy

$\sum_{j=1}^{71}\frac{x_{j}}{i+j}=\frac{4}{2i+1} \text{ for } i=1,2,...,71.$

Suppose $$\sum_{j=1}^{71}\frac{x_{j}}{2j+1} = \frac{p}{q},$$ where $$p$$ and $$q$$ are coprime integers. Find $$p+q$$.

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