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Question Number 13806 by ajfour last updated on 23/May/17

$$Provethatfor-\frac{\pi }{2}<x<\frac{\pi }{2},$$ $$\frac{1}{1^3}\cos x-\frac{1}{3^3}\cos 3x+\frac{1}{5^3}\cos 5x-....toinfinity$$ $$=\frac{\pi }{8}(\frac{{\pi }^2}{4}-x^2).$$

Commented byprakash jain last updated on 24/May/17

$$\mathrm{LHS}\mathrm{looks}\mathrm{like}\mathrm{fourier}\mathrm{series}$$ $$\mathrm{expansion}.$$ $$\mathrm{I}\mathrm{will}\mathrm{look}\mathrm{for}\mathrm{appropriate}\mathrm{function}$$ $$\mathrm{to}\mathrm{start}\mathrm{with}.$$

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