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Fourier series

{c}

On $(-\pi,\pi)$,
$$
x^3-\pi^2x
=12\sum_{n=1}^{\infty}\frac{(-1)^n}{n^3}\sin(nx).
$$
Parseval's identity and direct integration of the square give
$$
\sum_{n=1}^{\infty}\frac1{n^6}=\frac{\pi^6}{945}.
$$


Fourier series of x cubed minus pi squared x

Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 3A / Solution

Fourier series of x cubed minus pi squared x

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Fourier series of x cubed minus pi squared x

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