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advanced-calculus-prove-that-n-1-1-n-1-n-3-2n-n-2-5-3-




Question Number 145676 by mnjuly1970 last updated on 07/Jul/21
               ... advanced ......calculus...             prove that:                           Σ_(n=1) ^∞  (((−1)^(n−1) )/(n^( 3)   ((( 2n)),((   n)) ))) = (2/5) ζ (3 )
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{advanced}\:……{calculus}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\:\mathrm{3}} \:\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:\:{n}}\end{pmatrix}}\:=\:\frac{\mathrm{2}}{\mathrm{5}}\:\zeta\:\left(\mathrm{3}\:\right) \\ $$$$ \\ $$
Answered by Kamel last updated on 09/Jul/21
Answered by Kamel last updated on 09/Jul/21

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