How do I show: $$\zeta {\space(3)} = \frac{5}{2} \sum_{n=1}^{\infty}{\frac{(-1)^{n-1}}{{{n^3}{2n\choose{n}}}}}$$ and if I want to generalize for any value of the zeta function what do I have to change, the $n^3$ term?
2026-03-30 06:32:43.1774852363
Proof that $\zeta {\space(3)} = \frac{5}{2} \sum{(-1)^{n-1}/{n^3}{2n\choose{n}}}$ and generalizations.
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