- #1

CricK0es

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**< Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown >**

Hi all. I'm completely new to these forums so sorry if I'm doing anything wrong.

Anyway, I have this question...

Find the Fourier series for the periodic function

f(x) = x^2 (-pi < x < pi), f(x) = f(x+2pi)

By considering the particular values x = 0 and x = +/- pi prove that

f(x) = x^2 (-pi < x < pi), f(x) = f(x+2pi)

By considering the particular values x = 0 and x = +/- pi prove that

∞^Σ (n=1) 1 / n^2 = pi^2 / 6

and

∞^Σ (n=1) (-1)^n / n^2 = -pi^2 / 12

I missed a couple of lectures due to illness so I'm not entirely sure what to do with this.

Again, I'm really sorry that it's all a bit messy but I'm still getting use to everything. I would like to learn how to use LaTeX to make equations easier/clearer also. But, regardless, I would really appreciate some guidance on how to proceed through the question. Many thanks

and

∞^Σ (n=1) (-1)^n / n^2 = -pi^2 / 12

I missed a couple of lectures due to illness so I'm not entirely sure what to do with this.

But I have worked through and found the FS itself. Whether it's right I really don't know...

= pi^2 / 3 + ∞^Σ (n=1) 4/n (-1)^n Cos(nx)But I have worked through and found the FS itself. Whether it's right I really don't know...

= pi^2 / 3 + ∞^Σ (n=1) 4/n (-1)^n Cos(nx)

Again, I'm really sorry that it's all a bit messy but I'm still getting use to everything. I would like to learn how to use LaTeX to make equations easier/clearer also. But, regardless, I would really appreciate some guidance on how to proceed through the question. Many thanks

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