Calculate sequence using the Fourier sequence?

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manpreet Tuteehub forum best answer Best Answer 2 years ago

 

I've been learning Fourier sequence for a while and now I'm stuck. I have a function

f(x)=x2,x[π,π]f(x)=x2,x∈[−π,π]
and once evaluating this to Fourier we get:
f(x)=π23+4n=1(1)nn2cos(nx)f(x)=π23+4∑n=1∞(−1)−nn2cos⁡(nx)

 

Now it says: with the aid of the Fourier sequence (above) calculate the following sequence:

n=11n4∑n=1∞1n4

 

How do I tackle such problem, I've goggled everything but haven't found anything similar.
Any help on this?

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