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:
\( H_n\) denotes the \(n^\text{th} \) harmonic number, \( H_n = 1 + \dfrac12 + \dfrac13 + \cdots + \dfrac1n\).
\(\zeta(\cdot) \) denotes the Riemann zeta function.
by
Refaat M. Sayed