<s>[INST] Given $\frac{1}{1^4}+\frac{1}{2^4}...\infty=\frac{\pi^4}{90}$ If $$\frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}...\infty=\frac{\pi^4}{90}$$
then, $$\frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}...\infty=?$$
Please provide a hint instead of the complete answer. Thanks. [Please edit the tags for me as I have no idea which sector this problem lies in.]
 [/INST] \begin{eqnarray*}
S_{even}=\sum_{i=1}^{\infty} \frac{1}{(2i)^4} = \frac{1}{16} S_{All} \\
S_{Odd}=\sum_{i=1}^{\infty} \frac{1}{(2i-1)^4} 
\end{eqnarray*}
and of course $S_{even}+S_{Odd}=S_{All}$.
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