Omg So much big series!

Calculus Level 3

\[ \large \displaystyle \lim_{x \to -1} \dfrac{(1+x)(1-x^2)(1+x^3)(1-x^4) \cdots (1-x^{4n})}{[(1+x)(1-x^2)(1+x^3)(1-x^4) \cdots (1-x^{2n})]^{2}} \]

If the limit above can be expressed in the form \( \dbinom{pn}{qn}\) for positive integers \(p,q,n\), find the value of \(p + q\).

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