I calculate bn like this: I know that the answer should be What am I doing wrong

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First: the function is odd over the interval, so only sines should be there in the series. ----> but you actually solved for the cosines. Second: we expect the coefficient of the cosines to vanish but you get a nonzero answer. What's the problem? Your interval for your integration should be from -pi to pi I solved the problem and I got the same answer as the book. I will just give you hints: (ok? your doing good already) We wish to represent f(t) in terms of fourier series in the interval -pi to pi f(t) = t = A0 + SUM An Cos nt + SUM Bn sin nt as you said, the An's should vanish. So we only need to find Bn's Which is done by multiplying the equation by sin mt. note (not cosine!) This is to take advantage of the orthogonality condition INTEGRAL sin nt * sin mt dt = constant * kronecker delta of nm if you have not done this, skip to the result. (constant = pi) -----------> Bn = 1/pi INTEGRAL f(t) sin nt dt over -pi to pi (I think you can find this in the book but be careful, the constant = pi depends on the interval) (maybe im wrong, just check with your textbook) Then the rest is computations. Integration by parts but the second part is actually zero and you will be left with something like -------------> Bn = [-pi (-1)^n + pi (-1)^n]/n pi then you have the anwer. Hope I helped. Sorry, Im not using proper equations. I know you can get it!

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