Question Number 55920 by ANTARES VY last updated on 06/Mar/19
$$\boldsymbol{\mathrm{Calculate}}. \\ $$$$\underset{\boldsymbol{{a}}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\boldsymbol{{b}}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\boldsymbol{{c}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\boldsymbol{{ab}}\left(\mathrm{3}\boldsymbol{{a}}+\boldsymbol{{c}}\right)}{\mathrm{4}^{\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}} \left(\boldsymbol{{a}}+\boldsymbol{{b}}\right)\left(\boldsymbol{{b}}+\boldsymbol{{c}}\right)\left(\boldsymbol{{c}}+\boldsymbol{{a}}\right)}. \\ $$
Commented by mr W last updated on 06/Mar/19
$$\frac{\mathrm{1}}{\mathrm{54}} \\ $$$${can}\:{someone}\:{prove}? \\ $$