# Inspired by Patrick Corn

Calculus Level 5

$\large \displaystyle\sum \limits^{\infty }_{n=1}\dfrac{( -1) ^{n-1}H_{n}}{n}$

If the series above is equal to $\dfrac{\zeta ( A) }{B} -\dfrac{(\ln D)^C }{E} ,$ where $$A$$, $$B$$, $$C$$, $$D$$ and $$E$$ are all positive integers, find $$A+B+C+D+E$$.

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