I'm trying to show that the Fourier series of [itex] f(x)=x^2[/itex] converges and I can't. Does anybody know if it actually does converge? (I'm assuming that [itex] f(x)=x^2[/itex] for [itex] x\in [-\pi,\pi][/itex]).(adsbygoogle = window.adsbygoogle || []).push({});

The Fourier Series itself is [itex] \displaystyle\frac{\pi^2}{3}+4\sum_{n=1}^\infty \frac{(-1)^n}{n^2}\cos nx [/itex]

I tried using Dirichlet's test but it wasn't working for me, though that may be because I'm doing something wrong.

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# Does Fourier series of x^2 converge?

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