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Question Number 159045 by amin96 last updated on 12/Nov/21

$$\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{{(3n+1)}^3}=?$$

Answered by mindispower last updated on 16/Nov/21

$$=\sum _{n⩾0}.\frac{1}{27}\frac{1}{{(n+\frac{1}{3})}^3}$$$${\mathrm{\Psi }}^{\left(2\right)}\left(z\right)=2\sum _{n⩾0}\frac{1}{{(n+z)}^3}$$$$weget\frac{1}{54}{\mathrm{\Psi }}^{\left(2\right)}\left(\frac{1}{3}\right)$$

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