[tex] \sum _{n=1}^{\infty } \frac{1}{n^4} [/tex](adsbygoogle = window.adsbygoogle || []).push({});

I can do 1/n^2 easily by using x^2 as a function but for this I try

[tex] x^4=\frac{1}{2\pi }\int_{-\pi }^{\pi } x^4 \, dx+\sum _{n=1}^{\infty } \left(\frac{2}{\pi }\int _0^{\pi }x^4\text{Cos}[n x]dx\right)\text{Cos}[n x] [/tex]

I arrive at:

[tex] \pi ^4=\frac{\pi ^4}{5}+\sum _{n=1}^{\infty } \frac{8 \left(-6+n^2 \pi ^2\right)}{n^4 } [/tex]

[tex] \frac{4\pi ^4}{5}=\sum _{n=1}^{\infty } \frac{8 \left(-6+n^2 \pi ^2\right)}{n^4 } [/tex]

f(x) = x^4 does not seem helpful to sum 1/n^4, maybe I need a polynomial in x of degree 4?

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# Homework Help: Using fourier series to sum 1/n^4

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