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 \(A+B+C+D+E\).

Notations:


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