# 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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