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?
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The bounds are not there and the fraction is vague. $(a/b)c\stackrel?=a/bc\stackrel?=a/(bc)$ – Simply Beautiful Art May 04 '17 at 23:28
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Related: What is the binomial sum $\sum_{n=1}^\infty \frac{1}{n^5,\binom {2n}n}$ in terms of zeta functions? – Simply Beautiful Art May 04 '17 at 23:34
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Ok, will fix that now – mtheorylord May 05 '17 at 00:07