# Resembling Resemblence-4

Calculus Level 5

\begin{align}\displaystyle\sum_{k=1}^{\infty} \dfrac{(-1)^{k+1} H_{k}}{k}\end{align}=\dfrac{1}{2} \left(\zeta(P)-\log^2 (Q)\right)

If the above equation is satisfied by positive integers $$P$$ and $$Q$$. Find $$P^Q$$.

$$H_{n}$$ is the $$n^{th}$$ harmonic number.

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