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n-1-sin-2n-1-pi-6-2n-1-2-a-G-a-G-catalan-constant-




Question Number 141512 by mnjuly1970 last updated on 19/May/21
     Σ_(n=1 ) ^∞ ((sin((((2n−1)π)/6)))/((2n−1)^2 )) = a.G    a = ?      (G:= catalan constant)
$$ \\ $$$$\:\:\:\underset{{n}=\mathrm{1}\:} {\overset{\infty} {\sum}}\frac{{sin}\left(\frac{\left(\mathrm{2}{n}−\mathrm{1}\right)\pi}{\mathrm{6}}\right)}{\left(\mathrm{2}{n}−\mathrm{1}\right)^{\mathrm{2}} }\:=\:{a}.{G} \\ $$$$\:\:{a}\:=\:?\:\:\:\:\:\:\left({G}:=\:{catalan}\:{constant}\right) \\ $$$$ \\ $$

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