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What is the sum of the series [math]\sum_{n=1,3,5,\ldots}^\infty \frac{1}{n^4}[/math]?
That's interesting. Could you explain how it is derived?
It can be derived using the relationship between the Riemann zeta function and the Bernoulli numbers, where [math]\zeta(4)=\frac{\pi^4}{90}[/math] and the relationship [math]B_k=-k\zeta(1-k)[/math].