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Let $f(x)$ be a real, periodic function satisfying $f(-x)=-f(x)$. The general form of its Fourier series representation would be

  1. $f(x)=a_{0}+\sum_{k=1}^{\infty}a_{k}\cos(kx)$
  2. $f(x)=\sum_{k=1}^{\infty}b_{k}\sin(kx)$
  3. $f(x)=a_{0}+\sum_{k=1}^{\infty}a_{2k}\cos(kx)$
  4. $f(x)=\sum_{k=0}^{\infty}a_{2k+1}\sin(2k+1)x$
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