Question Number 146194 by mathmax by abdo last updated on 11/Jul/21
$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{3}} \mathrm{5}^{\mathrm{n}} } \\ $$
Answered by qaz last updated on 12/Jul/21
$$\underset{\mathrm{1}\leqslant\mathrm{n}\leqslant\infty} {\sum}\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{3}} \mathrm{5}^{\mathrm{n}} }=\mathrm{Li}_{\mathrm{3}} \left(\frac{\mathrm{1}}{\mathrm{5}}\right) \\ $$