Fourier Series. Writing a partial sum as an integral.

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Homework Statement



Given: View attachment 56653, show that this can be written as: View attachment 56651.

Homework Equations



Hint: View attachment 56652

The Attempt at a Solution



Quite confused by this question. For f'N I have:

[itex]\frac{4}{∏}[/itex]Ʃ[itex]\frac{cos((2n -1)x)}{(2n - 1)^{2}}[/itex] but i'm not sure where to go from here.

I have read about the Dirichlet kernel, which is what I think I require, but I am rather lost.

Any help is appreciated.

Cheers.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Attachments

  • hint.png
    hint.png
    4.8 KB · Views: 371
  • integral.png
    integral.png
    3.1 KB · Views: 324
  • partial sum.png
    partial sum.png
    3.1 KB · Views: 330

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