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nice-calculus-prove-that-n-1-1-n-1-n-3-2n-n-3-m-n-1970-




Question Number 119445 by mnjuly1970 last updated on 24/Oct/20
          ...nice  calculus...   prove  that::              Σ_(n=1) ^∞ (((−1)^(n−1) )/(n^3  (((2n)),(n) ))) =^(???) ζ(3)             m.n.1970
$$\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\mathrm{3}} \begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}}\:\overset{???} {=}\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$

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