Denote the Fourier series of f(x)=\left\{\begin{array}{ll} -x, & -\pi \leq x<0 \\ x, & 0 \leq x<\pi \end{array}\right. by F(x), where F(x) has a period 27. Show that F(x)=\frac{\pi}{2}-\frac{4}{\pi} \sum_{m=1}^{\infty} \frac{\cos (2 m-1) x}{(2 m-1)^{2}} \text { For }-2 \pi<x<2 \pi \text { siketch the graph of } F(x) Deduce that 1+\frac{1}{3^{2}}+\frac{1}{5^{2}}+\cdots=\frac{\pi^{2}}{8}

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