# Even harmonic?

Calculus Level 5

$\large \sum_{n=1}^\infty (-1)^{n-1} \dfrac{H_{2n}}n = \dfrac{A\pi^B}C - \dfrac{(\ln B)^2}D$

If the equation above holds true for positive integers $$A,B,C$$ and $$D$$ with $$A,C$$ coprime, find $$A+B+C+D$$.

 Notation: $$H_n$$ denotes the $$n^\text{th}$$ harmonic number, $$H_n = 1 + \dfrac12 + \dfrac13 + \cdots + \dfrac1n$$.

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