Question Number 99895 by bachamohamed last updated on 23/Jun/20
$$\:\:\:\:\underset{\boldsymbol{{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{3}\boldsymbol{{n}}+\mathrm{1}\right)^{\mathrm{3}} }=\frac{\mathrm{13}}{\mathrm{27}}\:\boldsymbol{\zeta}\left(\mathrm{3}\right)\:+\frac{\mathrm{2}\boldsymbol{\pi}^{\mathrm{3}} }{\mathrm{81}\sqrt{\mathrm{3}}}\: \\ $$
Answered by maths mind last updated on 24/Jun/20