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ln423+ln633+ln843+ln1053+⋯\dfrac{\ln 4}{2^{3}} + \dfrac{\ln 6}{3^{3}} + \dfrac{\ln 8}{4^{3}} + \dfrac{\ln 10}{5^{3}} + \cdots 23ln4+33ln6+43ln8+53ln10+⋯
You may use the approximations: ζ(3)≈1.2020569\zeta(3)\approx 1.2020569ζ(3)≈1.2020569 and ζ′(3)≈−0.198126 \zeta'(3)\approx-0.198126ζ′(3)≈−0.198126.
Notation: ζ(⋅)\zeta(\cdot) ζ(⋅) denotes the Riemann zeta function.
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