Who Let The Logarithms In?

Calculus Level 5

\[\dfrac{\ln 4}{2^{3}} + \dfrac{\ln 6}{3^{3}} + \dfrac{\ln 8}{4^{3}} + \dfrac{\ln 10}{5^{3}} + \cdots \]

You may use the approximations:
\(\zeta(3)\approx 1.2020569\) and \( \zeta'(3)\approx-0.198126\).

Notation: \(\zeta(\cdot) \) denotes the Riemann zeta function.

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