# Harmony in the world!

Calculus Level 5

$\large \displaystyle \sum_{k=1}^{\infty} \dfrac{(-1)^{(k+1)}H_{k}}{k}$

If the above sum can be expressed in the form $\large \dfrac{\zeta(P)}{R} - \dfrac{\ln^{2} R}{P} \; ,$ where $$P$$ and $$R$$ are positive integers, find $$P+R$$.

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

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