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Homework Statement
Consider the function φ(x) ≡ x on (0, l). Find the sum of the first three (nonzero) terms of its Fourier sine series.
Reference: Strauss PDE exercise 5.1.3
Homework Equations
The Attempt at a Solution
I have found the coefficient without difficulty, it is A_{n}= -2l/n\pi cos (n\pi) + 2/n^{2}\pi^{2} sin (n\pi).
When I plug in n=1,2,3; I obtain 2l/\pi, -2l/\pi and 2l/3\pi, respectively.
However the answer is given by: 2l/\pi sin (\pix/l) - 2l/\pi sin (2\pix/l) + 2l/3\pi sin (3\pix/l)
What I found comes from A_{n} for n=1,2,3 but I do not understand which those sine terms come from.
Thanks in advance